Journal articles on the topic 'Bilinear programs'
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1
Hansen, Pierre, and Brigitte Jaumard. "Reduction of indefinite quadratic programs to bilinear programs." Journal of Global Optimization 2, no. 1 (1992): 41–60. http://dx.doi.org/10.1007/bf00121301.
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Petrik, M., and S. Zilberstein. "A Bilinear Programming Approach for Multiagent Planning." Journal of Artificial Intelligence Research 35 (June 24, 2009): 235–74. http://dx.doi.org/10.1613/jair.2673.
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Multiagent planning and coordination problems are common and known to be computationally hard. We show that a wide range of two-agent problems can be formulated as bilinear programs. We present a successive approximation algorithm that significantly outperforms the coverage set algorithm, which is the state-of-the-art method for this class of multiagent problems. Because the algorithm is formulated for bilinear programs, it is more general and simpler to implement. The new algorithm can be terminated at any time and-unlike the coverage set algorithm-it facilitates the derivation of a useful online performance bound. It is also much more efficient, on average reducing the computation time of the optimal solution by about four orders of magnitude. Finally, we introduce an automatic dimensionality reduction method that improves the effectiveness of the algorithm, extending its applicability to new domains and providing a new way to analyze a subclass of bilinear programs.
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Ma, Chao, Haiying Gao, and Duo Wei. "A CP-ABE Scheme Supporting Arithmetic Span Programs." Security and Communication Networks 2020 (March 16, 2020): 1–16. http://dx.doi.org/10.1155/2020/3265871.
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Attribute-based encryption achieves fine-grained access control, especially in a cloud computing environment. In a ciphertext-policy attribute-based encryption (CP-ABE) scheme, the ciphertexts are associated with the access policies, while the secret keys are determined by the attributes. In recent years, people have tried to find more effective access structures to improve the efficiency of encryption systems. This paper presents a ciphertext-policy attribute-based encryption scheme that supports arithmetic span programs. On the composite-order bilinear group, the security of the scheme is proven by experimental sequence based on the combination of composite-order bilinear entropy expansion lemma and subgroup decision (SD) assumption. And, it is an adaptively secure scheme with constant-size public parameters.
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Kang, Ji-Hoon, Ki-Hyung Hong, Kyu-Young Whang, and Jung-Wan Cho. "Generalization of ZYT-linearizability for bilinear datalog programs." Information and Computation 188, no. 1 (January 2004): 77–98. http://dx.doi.org/10.1016/s0890-5401(03)00172-x.
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Al-Khayyal, F. A. "Jointly constrained bilinear programs and related problems: An overview." Computers & Mathematics with Applications 19, no. 11 (1990): 53–62. http://dx.doi.org/10.1016/0898-1221(90)90148-d.
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Hasan, M. M. Faruque, and I. A. Karimi. "Piecewise linear relaxation of bilinear programs using bivariate partitioning." AIChE Journal 56, no. 7 (November 30, 2009): 1880–93. http://dx.doi.org/10.1002/aic.12109.
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Dey, Santanu S., Asteroide Santana, and Yang Wang. "New SOCP relaxation and branching rule for bipartite bilinear programs." Optimization and Engineering 20, no. 2 (September 21, 2018): 307–36. http://dx.doi.org/10.1007/s11081-018-9402-9.
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Quesada, Ignacio, and Ignacio E. Grossmann. "A global optimization algorithm for linear fractional and bilinear programs." Journal of Global Optimization 6, no. 1 (January 1995): 39–76. http://dx.doi.org/10.1007/bf01106605.
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Kolodziej, Scott, Pedro M. Castro, and Ignacio E. Grossmann. "Global optimization of bilinear programs with a multiparametric disaggregation technique." Journal of Global Optimization 57, no. 4 (January 3, 2013): 1039–63. http://dx.doi.org/10.1007/s10898-012-0022-1.
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Al-Khayyal, Faiz A. "Note on solving linear complementarity problems as jointly constrained bilinear programs." Journal of Mathematical Analysis and Applications 158, no. 2 (July 1991): 583–89. http://dx.doi.org/10.1016/0022-247x(91)90259-3.
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Wicaksono, Danan Suryo, and I. A. Karimi. "Piecewise MILP under- and overestimators for global optimization of bilinear programs." AIChE Journal 54, no. 4 (2008): 991–1008. http://dx.doi.org/10.1002/aic.11425.
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Hu, Wuhua, and Wee Peng Tay. "An integer linear programming approach for a class of bilinear integer programs." Operations Research Letters 42, no. 3 (May 2014): 226–30. http://dx.doi.org/10.1016/j.orl.2014.03.002.
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Obiri, Isaac Amankona, Qi Xia, Hu Xia, Kwame Opuni-Boachie Obour Agyekum, Kwame Omono Asamoah, Emmanuel Boateng Sifah, Xiaosong Zhang, and Jianbin Gao. "A Fully Secure KP-ABE Scheme on Prime-Order Bilinear Groups through Selective Techniques." Security and Communication Networks 2020 (November 29, 2020): 1–18. http://dx.doi.org/10.1155/2020/8869057.
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Key-policy attribute-based encryption (KP-ABE) is the cryptographic primitive which enables fine grained access control while still providing end-to-end encryption. Although traditional encryption schemes can provide end-to-end encryption, users have to either share the same decryption keys or the data have to be stored in multiple instances which are encrypted with different keys. Both of these options are undesirable. However, KP-ABE can provide less key overhead compared to the traditional encryption schemes. While there are a lot of KP-ABE schemes, none of them simultaneously supports multiuse of attributes, adaptive security, monotone span programs, and static security assumption. Hence, we propose a fully secure KP-ABE scheme for monotone span programs in prime-order group. This scheme uses selective security proof techniques to obtain the requisite ingredients for full security proof. This strengthens the correlation between selective and full security models and enables the transition of the best qualities in selective security models to fully secure systems. The security proof is based on decisional linear assumption and three-party Diffie–Hellman assumption.
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Ruiz, Juan P., and Ignacio E. Grossmann. "Strengthening of lower bounds in the global optimization of Bilinear and Concave Generalized Disjunctive Programs." Computers & Chemical Engineering 34, no. 6 (June 2010): 914–30. http://dx.doi.org/10.1016/j.compchemeng.2009.10.016.
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Wu, Jia, and Liwei Zhang. "On Properties of the Bilinear Penalty Function Method for Mathematical Programs with Semidefinite Cone Complementarity Constraints." Set-Valued and Variational Analysis 23, no. 2 (October 1, 2014): 277–94. http://dx.doi.org/10.1007/s11228-014-0295-2.
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Coxon, Bruce. "Two-dimensional POMMIE carbon–proton chemical shift correlated 13C NMR spectrum editing." Canadian Journal of Chemistry 68, no. 7 (July 1, 1990): 1145–50. http://dx.doi.org/10.1139/v90-177.
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Two pulse sequences are described for acquisition of two-dimensional, carbon–proton chemical shift correlated 13C NMR spectra by the "phase oscillations to maximize editing technique". One of these sequences provides two-dimensional, carbon–proton chemical shift correlated spectra in which the 1H–1H coupling constants are present in the 1H chemical shift dimension, whereas the other sequence includes a bilinear rotation decoupling unit that removes the vicinal 1H–1H couplings in this dimension. Extensions of these techniques to generation of two-dimensional, carbon–proton chemical shift correlated CH, CH2, and CH313C NMR subspectra from linear combinations of three two-dimensional data sets are described. Decreased residual signals in the edited 2D subspectra have been achieved by Pascal programs that include six floating point coefficients, and a method for their calibration is discussed. Results are reported for troleandomycin (1). Keywords: 13C nuclear magnetic resonance, carbon–proton chemical shift correlation, DEPT, Pascal programs, POMMIE, two-dimensional NMR spectrum editing, troleandomycin.
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Vasic, Mirjana, Jelica Gvozdanovic-Varga, Miroslav Zoric, Marija Kraljevic-Balalic, and Janko Cervenski. "Analysis of grain size in bean (Phaseolus vulgaris L.) by linear and bilinear models." Genetika 42, no. 3 (2010): 535–44. http://dx.doi.org/10.2298/gensr1003535v.
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Bean grain size, along with grain color and shape, is a constituent of bean?s market quality. In order to be able to satisfy the broad market demand, cultivars with grain of all classes (from the smallest to largest) and top agronomic qualities must be developed. This paper analyzed 24 bean genotypes. They had different grain size in terms of their specific responses to growing conditions over three growing seasons. The two-way ANOVA was used to separate the main effects responsible for the formation of grain of a particular size. The genotype effects were 89.9%, the year effects 2.2%, and those of genotype x year interaction 7.9%. A large portion of interaction variability was attributable to two (AMMI) or tree (SREG) highly significant (by the Gollob F-test) principal components. Most of the genotypes exhibited high stability. The various types of interactions between individual genotypes and growing conditions in a given year are shown in two types of biplot graphs (GE and GGE).t to introduce organic agriculture programs in breeding institutions.
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Qiu, Yongjian, Yuming Zhu, and Jingben Yin. "Branch-and-Reduction Algorithm for Indefinite Quadratic Programming Problem." Complexity 2021 (March 30, 2021): 1–14. http://dx.doi.org/10.1155/2021/5578427.
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This paper presents a rectangular branch-and-reduction algorithm for globally solving indefinite quadratic programming problem (IQPP), which has a wide application in engineering design and optimization. In this algorithm, first of all, we convert the IQPP into an equivalent bilinear optimization problem (EBOP). Next, a novel linearizing technique is presented for deriving the linear relaxation programs problem (LRPP) of the EBOP, which can be used to obtain the lower bound of the global optimal value to the EBOP. To obtain a global optimal solution of the EBOP, the main computational task of the proposed algorithm involves the solutions of a sequence of LRPP. Moreover, the global convergent property of the algorithm is proved, and numerical experiments demonstrate the higher computational performance of the algorithm.
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Ruiz, Juan P., and Ignacio E. Grossmann. "Exploiting vector space properties to strengthen the relaxation of bilinear programs arising in the global optimization of process networks." Optimization Letters 5, no. 1 (August 19, 2010): 1–11. http://dx.doi.org/10.1007/s11590-010-0228-4.
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Han, Inhwan. "Modelling the tyre forces for a simulation analysis of a vehicle accident reconstruction." Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering 231, no. 1 (August 5, 2016): 16–26. http://dx.doi.org/10.1177/0954407016630449.
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This paper proposes a modified bilinear tyre force model for simulations of the vehicle dynamics, which is the core part in reconstruction analysis of vehicle collision accidents. The physical parameters involved were estimated using a statistical method based on experimental test results of the tyre forces. With an appropriate setting of the input data related to a tyre blowout, a simulation analysis of the dynamics of the vehicle which had suffered the tyre blowout was performed. The developed simulation analysis results for the dynamic behaviour of a vehicle with normal tyres with total locks or with a one-wheel lock and for vehicles with tyre blowouts when driving straight or turning corresponded well to the results of other commercial programs. The reliability of these results was proved by comparing them with the corresponding data for many vehicles involved in blowout-related accidents and in particular the path travelled by those vehicles as recorded on black-box footages.
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Rana, Zaid Ashraf, Cheng Seong Khor, and Haslinda Zabiri. "Computational Experience with Piecewise Linear Relaxations for Petroleum Refinery Planning." Processes 9, no. 9 (September 9, 2021): 1624. http://dx.doi.org/10.3390/pr9091624.
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Refinery planning optimization is a challenging problem as regards handling the nonconvex bilinearity, mainly due to pooling operations in processes such as crude oil distillation and product blending. This work investigated the performance of several representative piecewise linear (or piecewise affine) relaxation schemes (referred to as McCormick, bm, nf5, and nf6t) and de (which is a new approach proposed based on eigenvector decomposition) that mainly give rise to mixed-integer optimization programs to convexify a bilinear term using predetermined univariate partitioning for instances of uniform and non-uniform partition sizes. The computational results showed that applying these schemes improves the relaxation tightness compared to only applying convex and concave envelopes as estimators. Uniform partition sizes typically perform better in terms of relaxation solution quality and convergence behavior. It was also seen that there is a limit on the number of partitions that contribute to relaxation tightness, which does not necessarily correspond to a larger number of partitions, while a direct relationship between relaxation size and tightness does not always hold for non-uniform partition sizes.
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EL-KHAMY, S. E., M. M. HADHOUD, M. I. DESSOUKY, B. M. SALAM, and F. E. ABD EL-SAMIE. "A NEW APPROACH FOR ADAPTIVE POLYNOMIAL BASED IMAGE INTERPOLATION." International Journal of Information Acquisition 03, no. 02 (June 2006): 139–59. http://dx.doi.org/10.1142/s0219878906000885.
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In this paper, an adaptive algorithm is suggested for the implementation of polynomial based image interpolation techniques such as Bilinear, Bicubic, Cubic Spline and Cubic O-MOMS. This algorithm is based on the minimization of the squared estimation error at each pixel in the interpolated image by adaptively estimating the distance of the pixel to be estimated from its neighbors. The adaptation process at each pixel is performed iteratively to yield the best estimate of this pixel value. This adaptive interpolation algorithm takes into consideration the mathematical model by which a low resolution (LR) image is obtained from a high resolution (HR) image. This adaptive algorithm is compared to traditional polynomial based interpolation techniques and to the warped distance interpolation techniques. The performance of this algorithm is also compared to the performance of other algorithms used in commercial interpolation softwares such as the ACDSee and the Photopro programs. Results show that the suggested adaptive algorithm is superior from the Peak Signal to Noise Ratio (PSNR) point of view to other traditional techniques and it has a higher ability of edge preservation than traditional image techniques. The computational cost of the adaptive algorithm is studied and found to be moderate.
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Ebell, Niklas, Andre Bott, Tobias Beck, Johannes Bürner, Julian Praß, and Jörg Franke. "Model of a Power-to-Gas System with Fuel Cell in a Mixed Integer Linear Program for the Energy Supply of Residential and Commercial Buildings." Applied Mechanics and Materials 871 (October 2017): 11–19. http://dx.doi.org/10.4028/www.scientific.net/amm.871.11.
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In the field of energy supply for residential and commercial buildings, the optimal operation,system configuration and sizing of generation as well as storage technologies are essential stepsfor cost-efficient investments. In current research, flexibility options for electricity from growing renewableenergies attract attention. One of the considered options is the power-to-gas technology incombination with fuel cells. Linear Programs for optimal system operation exist for example for distributedenergy systems. In this study we propose a Mixed Integer Linear Program of a power-to-gasunit consisting of an electrolyzer, a fuel cell and a hydrogen storage. For the fuel cell a minimum loadand a non-linear efficiency curve is taken into account. The non-linear efficiency curve is approximatedby piecewise linearization. Bilinear products in the modeling of the efficiency curve are beingsubstituted to maintain full power plant sizing and operation functionality. Different fuels, such as naturalgas and hydrogen to be converted in the fuel cell, are implemented as well. As a result, we showthat a detailed model of the non-linear efficiency curve of a fuel cell leads to more accurate results concerningthe system operation. The configuration of system components in the observed energy systemchanges. Especially the battery system experiences a change in sizing and operation. However, solvingtime of the model is increasing dramatically. Our results demonstrate a valuable approach to comparethe results of a Linear Program to a Mixed Integer Linear Program. Hence giving the possibility toevaluate the necessity of detailed over simplified models regarding calculation of cost-effectiveness.
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Kong, Qingxia, Shan Li, Nan Liu, Chung-Piaw Teo, and Zhenzhen Yan. "Appointment Scheduling Under Time-Dependent Patient No-Show Behavior." Management Science 66, no. 8 (August 2020): 3480–500. http://dx.doi.org/10.1287/mnsc.2019.3366.
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This paper studies how to schedule medical appointments with time-dependent patient no-show behavior and random service times. The problem is motivated by our studies of independent datasets from countries in two continents that unanimously identify a significant time-of-day effect on patient show-up probabilities. We deploy a distributionally robust model, which minimizes the worst-case total expected costs of patient waiting and service provider’s idling and overtime, by optimizing the scheduled arrival times of patients. This model is challenging because evaluating the total cost for a given schedule involves a linear program with uncertainties present in both the objective function and the right-hand side of the constraints. In addition, the ambiguity set considered contains discrete uncertainties and complementary functional relationships among these uncertainties (namely, patient no-shows and service durations). We show that when patient no-shows are exogenous (i.e., time-independent), the problem can be reformulated as a copositive program and then be approximated by semidefinite programs. When patient no-shows are endogenous on time (and hence on the schedule), the problem becomes a bilinear copositive program. We construct a set of dual prices to guide the search for a good schedule and use the technique iteratively to obtain a near-optimal solution. Our computational studies reveal a significant reduction in total expected cost by taking into account the time-of-day variation in patient show-up probabilities as opposed to ignoring it. This paper was accepted by David Simchi-Levi, optimization.
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Raymond, Emma, Chandra A. Reynolds, Anna K. Dahl Aslan, Deborah Finkel, Malin Ericsson, Sara Hägg, Nancy L. Pedersen, and Juulia Jylhävä. "Drivers of Frailty from Adulthood into Old Age: Results from a 27-Year Longitudinal Population-Based Study in Sweden." Journals of Gerontology: Series A 75, no. 10 (April 29, 2020): 1943–50. http://dx.doi.org/10.1093/gerona/glaa106.
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Abstract Background Frailty is a strong predictor of adverse outcomes. However, longitudinal drivers of frailty are not well understood. This study aimed at investigating the longitudinal trajectories of a frailty index (FI) from adulthood to late life and identifying the factors associated with the level and rate of change in FI. Methods An age-based latent growth curve analysis was performed in the Swedish Adoption/Twin Study of Aging (N = 1,842; aged 29–102 years) using data from up to 15 measurement waves across 27 years. A 42-item FI was used to measure frailty at each wave. Results A bilinear, two-slope model with a turning point at age 65 best described the age-related change in FI, showing that the increase in frailty was more than twice as fast after age 65. Underweight, obesity, female sex, overweight, being separated from one’s co-twin during childhood, smoking, poor social support, and low physical activity were associated with a higher FI at age 65, with underweight having the largest effect size. When tested as time-varying covariates, underweight and higher social support were associated with a steeper increase in FI before age 65, whereas overweight and obesity were associated with less steep increase in FI after age 65. Conclusions Factors associated with the level and rate of change in frailty are largely actionable and could provide targets for intervention. As deviations from normal weight showed the strongest associations with frailty, future public health programs could benefit from monitoring of individuals with abnormal BMI, especially those who are underweight.
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Wu, Chenchen, Dachuan Xu, and Jiawei Zhang. "Safe Approximations for Distributionally Robust Joint Chance Constrained Program." Asia-Pacific Journal of Operational Research 32, no. 01 (February 2015): 1540004. http://dx.doi.org/10.1142/s0217595915400047.
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In this paper, we present a bilinear second-order cone programming safe approximation for the distributionally robust chance constrained program (DRCCP), assuming that the support of the uncertain parameters, and the first and second marginal moments of the probability with respect to the interval constraint imposed on the sum of the uncertain parameters are given. If we further know the covariance matrix, we can obtain a bilinear semi-definite programming safe approximation. Preliminary numerical tests indicate that the proposed models are competitive.
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Gajanayake, Bandara, Brian W. Trader, K. Raja Reddy, and Richard L. Harkess. "Screening Ornamental Pepper Cultivars for Temperature Tolerance Using Pollen and Physiological Parameters." HortScience 46, no. 6 (June 2011): 878–84. http://dx.doi.org/10.21273/hortsci.46.6.878.
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Temperature affects reproductive potential, aesthetic, and commercial value of ornamental peppers (Capsicum annuum L.). Limited information is available on cultivar tolerance to temperature stress. An experiment was conducted using pollen and physiological parameters to assess high and low temperature tolerance in ornamental peppers. In vitro pollen germination (PG) and pollen tube length (PTL) of 12 morphologically diverse ornamental pepper cultivars were measured at a range of temperatures, 10 to 45 °C with 5 °C increments. Cell membrane thermostability (CMT), chlorophyll stability index (CSI), canopy temperature depression (CTD), and pollen viability (PV) were measured during flowering. From the modified bilinear temperature–PG and PTL response functions, cardinal temperatures (Tmin, Topt, and Tmax) for PG and PTL and maximum PG (PGmax) and PTL (PTLmax) were estimated. Cultivars varied significantly for PG, PTL, cardinal temperatures for PG and PTL, and all three physiological parameters. Cumulative temperature response index (CTRI) of each cultivar, calculated as the sum of 12 individual temperature responses derived from PV, PGmax, PTLmax, Tmin, Topt, and Tmax for PG and PTL, CMT, CTD, and CSI were used to distinguish differences among the cultivars and classify for high (heat) and low (cold) temperature tolerance. Based on CTRI–heat, cultivars were classified as heat-sensitive (‘Black Pearl’, ‘Red Missile’, and ‘Salsa Yellow’), intermediate (‘Calico’, ‘Purple Flash’, ‘Sangria’, and ‘Variegata’), and heat-tolerant (‘Chilly Chili’, ‘Medusa’, ‘Thai Hot’, ‘Explosive Ember’, and ‘Treasures Red’). Similarly, cultivars were classified for cold tolerance as cold-sensitive, moderately cold-sensitive, moderately cold-tolerant, and cold-tolerant based on CTRI–cold. ‘Red Missile’ and ‘Salsa Yellow’ were classified as cold-tolerant. Cultivar screening using pollen parameters will be ideal for reproductive temperature tolerance, whereas physiological parameters will be suitable for screening vegetative temperature tolerance. The identified heat- and cold-tolerant cultivars are potential candidates in breeding programs to develop new ornamental and vegetable pepper genotypes for high and low temperature tolerance.
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Mangasarian, O. L. "The linear complementarity problem as a separable bilinear program." Journal of Global Optimization 6, no. 2 (March 1995): 153–61. http://dx.doi.org/10.1007/bf01096765.
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Dexter, Franklin. "Observational Study of the Distribution and Diversity of Interventional Pain Procedures Among Hospitals in the State of Iowa." Pain Physician 3, no. 22;3 (May 11, 2019): E157—E170. http://dx.doi.org/10.36076/ppj/2019.22.e157.
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Background: Critical access hospitals represent 61% of hospitals in the rural United States, and 68% of hospitals in Iowa. The role of small hospitals, such as critical access hospitals, in providing interventional chronic pain procedures is unknown. Objectives: We evaluated whether: a) the diversity of interventional pain procedures offered by hospitals is related to their size and is attributable principally to lumbosacral epidural injections; b) critical access hospitals contribute substantively to the count and diversity of pain procedures; and c) whether most interventional pain procedures performed at hospitals’ facilities are performed by relatively few proceduralists or by the cumulative activity of many clinicians. Study Design: This research involved an observational cohort design with a sample size of n = 283,940 interventional pain procedures. Setting: Data were collected from hospital-owned facilities in the state of Iowa from July 2012 through September 2017. Methods: The diversity of types of interventional pain procedures performed statewide was quantified in terms of the relative proportions of procedures at each hospital using the Herfindahl index. Bilinear weighted least squares regression quantified the relationship between the inverse of the Herfindahl and the percentage of procedures that were lumbar or caudal epidural. Kendall tau concordances quantified the relationship between counts of interventional pain procedures and hospital size. Using a blinded version of the National Provider Identifier of the clinician with primary responsibility for performing the principal procedure of the ambulatory visit, we calculated the percentage shares of interventional pain procedures performed by the 1% and 5% of proceduralists who performed the most procedures. Results: The diversity of types of procedures substantively differentiated among hospitals. Heterogeneity among hospitals in the proportion of procedures that were lumbar or caudal epidural injections substantively contributed to the heterogeneity among hospitals (P < .001). Hospitals performing more procedures tended to have greater diversity of types of procedures (P < .001). However, the strength of the concordance was small (Kendall τb = 0.332), showing substantial heterogeneity among hospitals. The 82 critical access hospitals statewide cumulatively accounted for 23.9% of interventional pain procedures. The critical access hospitals’ procedures were mostly (67.7%) lumbar or caudal epidural injections (P < .001), greater than the 48.9% of the other 41 hospitals (P < .001). Procedures were concentrated among proceduralists. The 1.0% of the proceduralists performing the most procedures performed 64.8% of procedures. The 5.0% of proceduralists performing the most procedures performed 87.7% of procedures. Limitations: The data are procedures were performed in hospital-owned facilities of Iowa. Conclusions: Although busier pain programs, based on procedures per week, generally performed more types of procedures, the variability was so large that the number of procedures a pain program performs per week cannot validly be used to infer the diversity of the hospital’s pain medicine practice. Hospitals with pain medicine programs that lack diversity in the types of procedures performed may provide limited options for patients and be susceptible to changes in payment for individual procedures. Relatively few proceduralists performed the vast majority of the procedures. Key words: Critical access hospitals, Herfindahl, interventional pain procedures, managerial epidemiology, pain medicine, state outpatient procedure database, lumbar epidural
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Ito, Masaaki. "A reduce program for Hirota's bilinear operator and Wronskian operations." Computer Physics Communications 50, no. 3 (August 1988): 321–30. http://dx.doi.org/10.1016/0010-4655(88)90188-9.
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González Tamayo, Juan Pablo. "Diseño e implementación de controladores digitales a través de un sistema de adquisición de datos." Scientia et technica 21, no. 3 (September 30, 2016): 204. http://dx.doi.org/10.22517/23447214.10421.
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En este artículo se mostrarán los resultados de la implementación de diferentes controladores digitales, como el PID con transformación bilineal y el control por ubicación de polos mediante la realimentación de estados, en una planta identificada de segundo orden; para lo cual se emplea un sistema de adquisición de datos, que se programa desde el entorno de desarrollo Matlab.
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Perera, Nandana, Bahram Gharabaghi, and Peter Noehammer. "Stream Chloride Monitoring Program of City of Toronto: Implications of Road Salt Application." Water Quality Research Journal 44, no. 2 (May 1, 2009): 132–40. http://dx.doi.org/10.2166/wqrj.2009.014.
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Abstract In cold regions, winter road safety is a major challenge for municipalities and provincial highway transportation agencies. Road salt is widely used to improve winter road conditions, but concerns have been raised about the effects of road salts on the environment. This paper describes a water quality monitoring program designed to measure both background chloride concentrations and the effects of road salt application on stream water quality in four watersheds (Humber River, Don River, Highland Creek, and Morningside tributary of Rouge River) located within the City of Toronto boundary. The effect of road salts on stream water quality was evaluated based on chloride concentration because of its conservative nature. A bilinear correlation was developed to transform measured specific conductance levels in stream water to chloride concentrations. There are no Ontario aquatic fresh water quality guidelines for chloride, but chloride concentrations in almost all the monitored streams in Toronto periodically exceeded chronic and acute chloride threshold levels of the United States Environmental Protection Agency. The City of Toronto has been proactive in its efforts to implement management practices to reduce the impact of road salt application on the environment while maintaining safe driving conditions for its road users. Normalized salt application rates in Toronto have been on a gradual declining trend in the last decade from about 0.08 to 0.07 tonnes of salt applied per centimetre of snowfall per kilometre of lane. With public safety in mind, further reductions in salt application rates are being considered to reduce the adverse environmental effects to acceptable limits.
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Zaharov, A., and Y. Zakharova. "Content of the “Geometric Modeling” Course for the “Mathematics and Computer Science” Training Program." Geometry & Graphics 9, no. 4 (April 14, 2022): 35–45. http://dx.doi.org/10.12737/2308-4898-2022-9-4-35-45.
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In this paper has been considered the main content and distinctive features of the “Geometric Modeling” training course for the “Mathematics and Computer Science” training program 02.03.01 (“Mathematical and Computer Modeling” specialization).
The goal of the “Geometric Modeling” course study is the assimilation of mathematical methods for construction of geometric objects with complex curved shapes, and techniques for their computer visualization by using polygons of curves and surfaces. Methods for construction of structures’ curved shapes using spline representations, as well as techniques for construction of surfaces and volumetric geometries using motion operations and basic logical operations on geometric objects are considered. The spline representations include linear and bilinear splines, Hermite cubic splines and Hermite surfaces, natural cubic and bicubic interpolation splines, Bezier curves and surfaces, rational Bezier splines, B-splines and B-spline surfaces, NURBS-curves and NURBS-surfaces, transfinite interpolation methods, and splines of surfaces with triangular form. Logical operations for intersection of two spline curves, and intersection of two parametric surfaces are considered. The principles of scientific visualization and computer animation are considered in this course as well.
Some examples for visualization of initial data and results of curves and surfaces construction in two- and three-dimensional spaces through the software shell developed by authors and used by students while doing tests have been demonstrated. The software shell has a web interface with the WebGL library graphic support. Tasks for four practical studies in a computer classroom, as well as several variations of homework are represented.
The problems occurring in preparation materials for some course sections are discussed, as well as the practical importance of acquired knowledge for the further progress of students.
The paper may be interesting for teachers of “Geometric Modeling” and “Computer Graphics” courses aimed to students with a specialization in mathematics and information, as well as to those who independently develop software interfaces for algorithms of geometric modeling.
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Silva, Alessandra Querino da, Luciano Antonio de Oliveira, Carlos Pereira da Silva, Cristian Tiago Erazo Mendes, Elias Silva de Medeiros, and Thelma Sáfadi. "Aplicação do modelo AMMI-bayesiano no estudo de estabilidade e adaptabilidade genotípica em dados de mostarda." Research, Society and Development 9, no. 9 (August 14, 2020): e166997023. http://dx.doi.org/10.33448/rsd-v9i9.7023.
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A análise de conjuntos de dados provenientes de ensaios multiambientais é de fundamental importância nas fases finais dos programas de melhoramento de plantas. Nesse contexto, o Modelo de Efeitos Principais Aditivos e Interação Multiplicativa (AMMI) se tornou um método popular para avaliar respostas de genótipos em diversos ambientes. No presente trabalho aplicou-se o modelo AMMI, sob o enfoque bayesiano, a um conjunto de dados provenientes de um experimento em blocos casualizados com 12 genótipos (variedades) de mostarda em 6 ambientes distintos. O objetivo foi analisar estabilidade e adaptabilidade genotípica por meio da representação biplot AMMI-2, ressaltando diferenças dessa abordagem em relação a análise AMMI-clássica. Os resultados evidenciaram a grande flexibilidade do método bayesiano para incorporar efeito aleatório para genótipos, bem como inferência ao biplot por meio de regiões de credibilidade para escores genotípicos e ambientais que descrevem o efeito da interação genótipos por ambientes (GEI). As regiões de credibilidade construídas para efeitos principais e parâmetros bilineares permitiram identificar genótipos mais produtivos e visualizar subgrupos homogêneos de genótipos e ambientes em relação ao efeito da GEI. Os genótipos mais produtivos foram G8 e G10 e apenas o G2 foi considerado estatisticamente estável.
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Miramontes de León, Diego, Omar Merabet, and Jean Reynouard. "MODELLING THE CYCLIC RESPONSE OF RC BEAM-COLUMN MEMBERS." Revista de Ingeniería Sísmica, no. 64 (January 1, 2001): 19. http://dx.doi.org/10.18867/ris.64.200.
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La mayoría de los modelos cíclicos uniaxiales formulados en variables globales (M, φ) toman en cuenta varios fenómenos esenciales de las secciones de Concreto Reforzado. Sin embargo, a menudo se asumen descargas elásticas lineales. Esta suposición involucra una disipación nula deenergía para cargas cíclicas no alternantes, mientras que los resultados observados muestran degradación de resistencia y disipación de energía. Más aun, para cargas cíclicas alternantes como las sísmicas, la disipación de energía observada está relacionada con el comportamiento no lineal tanto en carga como en descarga. La falta de atención a este comportamiento producedeformaciones residuales más pequeñas y, en consecuencia, un comportamiento histerético diferente. Con el propósito de lograr una predicción más realista, se incluye un comportamiento de descarga bilineal a una ley cíclica. El trabajo está basado en un modelo previamente implementado en el programa de uso general CASTEM2000 del Comisariado Francés para la Energía Atómica (CEA). El modelo se caracteriza por una curva envolvente trilineal y un conjunto de reglas cíclicas.La pérdida de rigidez y la degradación de resistencia tanto en la rama scendente como en la descendete y el amortiguamiento histerético dependen directamente del nivel e historia de carga aplicada. Las ecuaciones de movimiento se resuelven por el método de Newmark centrado y las condiciones de borde se imponen por medio de los multiplicadores de Lagrange. En este trabajo sedescribe la estrategia de análisis no lineal usando los multiplicadores de Langrange y el modelo cíclico propuesto. Los resultados numéricos se han comparado en experimentos con varios miembros estructurales y sub-ensambles sujetos a diferentes condiciones de carga. La comparación muestra el interés del modelo modificado propuesto.
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Bölükbaşı Macit, Zerrin. "In class activities family participation of developmental guidance programs prepared for 60-72 months children: Literature review60-72 Aylık çocuklar için hazırlanan gelişimsel rehberlik programlarında sınıf içi etkinliklerde aile katılımı: Literatür incelemesi." Journal of Human Sciences 14, no. 2 (June 1, 2017): 2001. http://dx.doi.org/10.14687/jhs.v14i2.4534.
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School Psychological Counseling and Guidance (PC&G) services have been working based on programs since 1990’s using comprehensive and developmental characteristics as base of PC&G. School PC&G studies, which first are providing services intended for the secondary education institutes, have started to provide services including pre-school period along with the “Lifelong and Developmental Concepts”. Because of the child’s 60-72 months’ period including; nursery class stage as the first step to school life, developable positive or negative behaviors regarding to the school and the risk of generalization of these behaviors through the further education life, it is further important that pre-school period PC&G services are given especially including families also. This study also comprises “Family Participation Method and Activities” that are used in pre-school period PC&G programs which also includes 60-72 months’ period. The compilation of information in consequence of the literature review has been examined in two titles, which are The Parents-Family Participation Concept and The Family Participation Types in PC&G Programs, and the information also found under these titles has been investigated. The acquired information from the literature review is that the Family Participation Activities are necessary to be included in the programs for every education level curriculum if they are to be efficient, functional, and lasting. As identified in Six Steps Family Participation Model, although first and second participation level and model applications of them comprised in School Wide Activities and Consultation Services sections, fourth participation level, in other words required to have been studied of School PC&G Programs’ classroom activities and family participation workings for the period of learning course at home have been encountered scarcely any in the literature. As a result, it is known reality that learning becomes permanent as the result of the recurrent actions. Consultation services are not given only for the family participation activities to reach of the any proficiency scopes of being prepared the pre-school PC&G Programs’, but also should be given to the classroom guidance activities’ family participation applications.Extended English abstract is in the end of PDF (TURKISH) file. ÖzetOkul Psikolojik Danışmanlık ve Rehberlik (PDR) hizmetleri, kapsamlı ve gelişimsel özelliklerini temele alarak çalışmaya başladığı 90’lı yıllardan bu yana program temelli olarak çalışmaktadır. İlk olarak orta öğretim kurumlarına yönelik olarak hizmet veren okul PDR çalışmaları “yaşam boyu ve gelişimsel” kavramları ile birlikte okul öncesi dönemi de kapsayacak şekilde hizmet vermeye başlamıştır. 60-72 ayın, çocuğun okula adım attığı anasınıfı dönemlerini de kapsaması, okula ilişkin geliştirebileceği olumlu ya da olumsuz tutumların oluşması, bu tutumların ileriki öğrenim yaşamına genellenme riskinin olması nedeni ile okul öncesi dönem rehberlik hizmetlerinin aileleri de programlarına dahil ederek verilmesi ayrıca önem taşımaktadır. Bu çalışmada 60-72 aylık yaş grubunu da kapsayan okul öncesi dönem PDR programlarında kullanılan aile katılımı yöntem ve etkinlikleri ile ilgili bilgilere yer verilmiştir. Literatür taraması sonucunda derlenen bilgiler I- Ebeveyn-aile katılımı kavramı, II- PDR programlarında aile katılımı türleri olmak üzere iki başlıkta incelenmiş ve bu başlıklar altında bulunan çalışmalar ile ilgili bilgiler incelenmiştir. İncelenen literatürün ifade ettiği, her bir eğitim düzeyinde yer alan müfredatın etkili, işlevsel ve kalıcı olabilmesi için programlarda aile katılımı etkinliklerine yer vermesinin elzem oluşudur. Altı basamaklı aile katılımı modelinde tanımlanan birinci ve ikinci katılım düzeyi ve örnek uygulamalarına okul kapsamlı etkinlikler ve konsültasyon hizmetlerinde yer verilirken, dördüncü katılım düzeyi yani evde öğrenme düzeyinde çalışılması gereken okul PDR programlarının sınıf içi etkinlikleri ile ilgili aile katılım çalışmalarına literatürde yok denecek kadar az rastlanmıştır. Sonuç olarak öğrenmenin yapılan tekrarlar sonucu kalıcı hale geldiği bilinen bir gerçektir. Hazırlanan okul öncesi PDR programlarında herhangi bir yeterlik alanına ulaşmak için aile katılım etkinliklerine yalnızca konsültasyon hizmeti kapsamında değil hazırlanan sınıf içi rehberlik etkinliklerinde de aile katılımı uygulamalarına mutlaka yer verilmesi gerekmektedir.
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Villarruel, Gissela, and Roberto Aguiar. "COMPARACIÓN DE ESTRUCTURAS RÍGIDAS CON ESTRUCTURAS FLEXIBLES SOBRE AISLADORES SÍSMICOS FPT." Ciencia 19, no. 1 (March 15, 2018): 120. http://dx.doi.org/10.24133/ciencia.v19i1.328.
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Se presenta el análisis sísmico, mediante los Métodos Espectral y Simplificado Lineal del ASCE 7-10, con una validación de resultados en el software estructural SAP2000 obteniendo una interfaz gráfica en 3D, aplicado al bloque estructural I ZE del nuevo edificio: “Vinculación con la Sociedad” de la Universidad de las Fuerzas Armadas ESPE - sede Santo Domingo, que tiene aisladores sísmicos de triple péndulo de fricción colocados sobre los plintos de cimentación. Se realiza un análisis sísmico espacial, para obtener: periodos, desplazamientos, fuerzas laterales y derivas en el centro de masas de cada piso, tanto con el Método Espectral como el Simplificado Lineal, calculados con el sistema computacional CEINCI-LAB y el programa comercial SAP2000, ejecutados para dos alternativas de cálculo que son: modelo 1 (columnas más aisladores sísmicos FPT, denominada Estructura Flexible), y modelo 2 (muros de corte, columnas de hormigón armado y aisladores sísmicos FPT denominada Estructura Rígida). Para ello en primer lugar se presenta el marco teórico del Método Simplificado Lineal, siguiendo lo prescrito en la norma de aislación Chile INN (2013) y en el ASCE 7-10, dónde considera que la superestructura va a desplazarse como un solo cuerpo rígido, es decir, trabaja como un sistema de un grado de libertad con un modelo constitutivo del aislador bilineal. Para el Método Espectral se trabajó con la curva establecida de tres fases, propuesta por Mc Vitty y Constantinou (2015) para el aislador sísmico de triple péndulo de fricción FPT.El análisis tanto para la Estructura Rígida como para la Flexible se lo realiza en los dos sentidos “X” y “Y”, para dos espectros: el de diseño DBE y el máximo considerado MCE.Finalmente, se comparan los resultados máximos probables para cada modelo calculado (Estructura Flexible y Estructura Rígida) con sus correspondientes cálculos estructurales según el Método Espectral, Simplificado Lineal y SAP2000; se observa cómo mejora considerablemente el comportamiento sismo resistente al tener Estructuras Rígidas de éste tipo. Palabras Claves.- Aisladores sísmicos de triple péndulo de fricción (FPT). Sismo DBE y MCE. Método Espectral. Método Simplificado Lineal. SAP2000.
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Metin Karaaslan, Mehtap, and Ayda Çelebioğlu. "Determination of healthy lifestyle behaviors of high school studentsLise öğrencilerinin sağlıklı yaşam biçimi davranışlarının belirlenmesi." Journal of Human Sciences 15, no. 2 (June 30, 2018): 1355. http://dx.doi.org/10.14687/jhs.v15i2.4895.
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This research was conducted as a descriptive study to determine the healthy lifestyle behaviors of high school students. The schools located in Rize Province were grouped (n: 9926). The number of samples was determined to be 370 according to the sample width formula, which is known as the number of individuals in the phase. A total of 449 volunteer students were selected from a high school in each group by simple random sampling method and the study was completed. To collect data, the personal information form and healthy lifestyle behaviors scale II, which were developed by the researcher, were used. The data were evaluated using percentile, ANOVA and t test. It was determined that the average score of healthy lifestyle behaviors scale II scores of the students was moderate with 128.06 ± 20.19. The average score of female students' health responsibility and interpersonal relationship scores were higher than male students (p <0.05). The average physical activity score of male students was found to be higher than that of female students (p <0.05). A significant positive correlation between the age of the students and the class with 'interpersonal relations' and the total score was found (p <0.05). The acquisition of positive health behaviors during the adolescence period is important to perform healthy behaviors in the future life of the individual. As a result of this study, it is suggested that education programs should be established to protect and improve the health of the students. Also, education should develop the self-efficacy of the students. Moreover, it should be conducted according to the low-scored areas and schools. Extended English summary is in the end of Full Text PDF (TURKISH) file.ÖzetBu araştırma, lise öğrencilerinin sağlıklı yaşam biçimi davranışlarının belirlenmesi amacıyla tanımlayıcı olarak gerçekleştirilmiştir. Rize il merkezinde bulunan okullar gruplandırılmıştır(n: 9926). Evrende birey sayısı bilinen örneklem genişliği formülüne göre örneklem sayısı 370 olarak belirlenmiş, her gruptaki birer liseden basit rastgele örneklem yöntemiyle toplam 449 gönüllü öğrenci ile çalışma tamamlanmıştır. Verilerin toplanmasında, araştırmacı tarafından oluşturulan kişisel bilgi formu ve sağlıklı yaşam biçimi davranışları ölçeği II kullanılmıştır. Veriler bilgisayar ortaminda yüzdelik, ANOVA ve t testi kullanılarak değerlendirilmiştir.Öğrencilerin sağlıklı yaşam biçimi davranışları ölçeği puan ortalamasının 128.06±20.19 ile orta düzeyde olduğu belirlenmiştir. Kız öğrencilerin sağlık sorumluluğu ve kişilerarası ilişkiler puan ortalaması erkek öğrencilerin puan ortalamasından yüksek bulunmuştur(p<0.05). Erkek öğrencilerin fiziksel aktivite puan ortalaması, kız öğrencilerin puan ortalamasından yüksek bulunmuştur(p<0.05). Öğrencilerin yaşı ve sınıf ile ‘kişilerarası ilişkiler’ ve toplam puan arasında pozitif yönde anlamlı ilişki saptanmıştır (p<0.05).Adölesan döneminde olumlu sağlık davranışlarının kazanılması bireyin ileriki yaşamında sağlıklı davranışlar gerçekleştirmesi açısından önem taşımaktadır. Bu çalışma sonucunda öğrencilerin sağlıklarını korumak ve geliştirmek için eğitim programları oluşturulması ve eğitimin özellikle öz- etkililiği geliştirici olması ve daha çok düşük puan alınan alanlara ve okullara göre yapılması önerilmektedir.
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Demiray, Ayşe, Nagihan İlaslan, and Ayşegül Açıl. "Evaluatıon of nursıng students 'attıtudes towards braın draın." Journal of Human Sciences 17, no. 2 (May 17, 2020): 632–41. http://dx.doi.org/10.14687/jhs.v17i2.5956.
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Aim: The study was carried out in a descriptive type in order to evaluate the attitudes of nursing students towards brain drain.
Method: The research was conducted with 589 nursing students studying at a public university and agreeing to participate in the study. The data were collected using “Descriptive Features Form” and “Brain Drain Attitude Scale in Nursing Students”. Descriptive statistics, independent samples t test and ANOVA test were used to analyze the data.
Findings: It was determined that more than half of the students were in the 20 years and below, female, single, 29.4 of them are studying in the first class, 77.6% of their families live in the city center and 45.0% of them have income above the minimum level. Also 81.8% of the students stated that they knew English as a foreign language, 61.1% of them knew foreign language in medium level and 94.1% did not participate in any student exchange program. The students' average score taken from the Brain Drain Attitude Scale in Nursing Students was found to be 42.98 ± 9.91. A statistically significant difference was found between the scale total score of the students and the class level where students study, the level of income, the level of known foreign language, and participation in student exchange programs (p <0.05).
Conclusion: It was determined that attitudes of nursing students towards brain drain were below average. In line with the results of the research, it is recommended to conduct similar studies with different sample groups.
Extended English summary is in the end of Full Text PDF (TURKISH) file.
Özet
Amaç: Çalışma, hemşirelik öğrencilerinin beyin göçüne yönelik tutumlarını değerlendirilmek amacı ile tanımlayıcı türde gerçekleştirilmiştir. Yöntem: Araştırma bir devlet üniversitesinde öğrenim gören ve çalışmayı katılmayı kabul eden 589 hemşirelik öğrencisi ile gerçekleştirilmiştir. Veriler “Tanımlayıcı Özellikler Formu” ve “Hemşirelik Öğrencilerinde Beyin Göçüne Yönelik Tutum Ölçeği” kullanılarak toplanmıştır. Verilerin analizinde tanımlayıcı istatistikler, independent samples t testi ve ANOVA testi kullanılmıştır.
Bulgular: Araştırmaya katılan öğrencilerin %59.1’ inin 20 yaş ve altında, 75.4’ ünün kadın, %99.2’ sinin bekar olduğu, 29.4’ ünün birinci sınıfta öğrenim gördüğü, %77.6’ sının ailesinin şehir merkezinde yaşadığı ve %45.0’ ının gelir durumunu asgari düzeyin üzerinde olduğu belirlenmiştir. Öğrencilerin %81.8’ i yabancı dil olarak İngilizce’ yi bildiğini, %61.1’ i orta düzeyde yabancı dil bildiğini ve %94.1’ i herhangi bir öğrenci değişim programına katılmadığını ifade etmiştir. Öğrencilerin, Hemşirelik Öğrencilerinde Beyin Göçüne Yönelik Tutum Ölçeği’ nden aldıkları puan ortalaması 42.98±9.91 olarak bulunmuştur. Öğrencilerin ölçek toplam puanı ile öğrenim gördükleri sınıf, gelir düzeyi, bilinen yabancı dil düzeyi ve öğrenci değişim programlarına katılma durumu arasında istatistiksel olarak anlamlı fark saptanmıştır (p<0.05).
Sonuç: Hemşirelik öğrencilerinin beyin göçüne yönelik tutumlarının ortalamanın altında olduğu belirlenmiştir. Araştırma sonucu doğrultusunda farklı örneklem grupları ile benzer çalışmalar yapılması önerilmektedir.
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Boussaïd, Nabile, Marco Caponigro, and Thomas Chambrion. "Which notion of energy for bilinear quantum systems?* *This work has been partially supported by INRIA Nancy-Grand Est. Second and third authors were partially supported by French Agence National de la Recherche ANR “GCM” program “BLANC-CSD”, contract number NT09-504590. The third author was partially supported by European Research Council ERC StG 2009 “GeCoMethods”, contract number 239748." IFAC Proceedings Volumes 45, no. 19 (2012): 226–30. http://dx.doi.org/10.3182/20120829-3-it-4022.00034.
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Fleig, Arthur, and Roberto Guglielmi. "Bilinear Optimal Control of the Fokker-Planck Equation**This work was partially supported by the EU under the 7th Framework Program, Marie Curie Initial Training Network FP7-PEOPLE-2010-ITN SADCO, GA 264735-SADCO, by the DFG project Model Predictive Control for the Fokker-Planck Equation, GR 1569/15-1, and by the INdAM through the GNAMPA Research Project 2015 ”Analisi e controllo di equazioni a derivate parziali nonlineari”." IFAC-PapersOnLine 49, no. 8 (2016): 254–59. http://dx.doi.org/10.1016/j.ifacol.2016.07.450.
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Gu, Xiaoyi, Santanu S. Dey, and Jean-Philippe P. Richard. "Lifting convex inequalities for bipartite bilinear programs." Mathematical Programming, January 24, 2022. http://dx.doi.org/10.1007/s10107-021-01759-3.
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BORGES, PEDRO, CLAUDIA SAGASTIZÁBAL, MIKHAIL SOLODOV, and ASGEIR TOMASGARD. "A distributionally ambiguous two-stage stochastic approach for investment in renewable generation." European Journal of Applied Mathematics, May 12, 2022, 1–21. http://dx.doi.org/10.1017/s0956792522000122.
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The optimal expansion of a power system with reduced carbon footprint entails dealing with uncertainty about the distribution of the random variables involved in the decision process. Optimisation under ambiguity sets provides a mechanism to suitably deal with such a setting. For two-stage stochastic linear programs, we propose a new model that is between the optimistic and pessimistic paradigms in distributionally robust stochastic optimisation. When using Wasserstein balls as ambiguity sets, the resulting optimisation problem has nonsmooth convex constraints depending on the number of scenarios and a bilinear objective function. We propose a decomposition method along scenarios that converges to a solution, provided a global optimisation solver for bilinear programs with polyhedral feasible sets is available. The solution procedure is applied to a case study on expansion of energy generation that takes into account sustainability goals for 2050 in Europe, under uncertain future market conditions.
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Berta, Mario, Francesco Borderi, Omar Fawzi, and Volkher B. Scholz. "Semidefinite programming hierarchies for constrained bilinear optimization." Mathematical Programming, April 15, 2021. http://dx.doi.org/10.1007/s10107-021-01650-1.
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AbstractWe give asymptotically converging semidefinite programming hierarchies of outer bounds on bilinear programs of the form $${\mathrm {Tr}}\big [H(D\otimes E)\big ]$$ Tr [ H ( D ⊗ E ) ] , maximized with respect to semidefinite constraints on D and E. Applied to the problem of approximate error correction in quantum information theory, this gives hierarchies of efficiently computable outer bounds on the success probability of approximate quantum error correction codes in any dimension. The first level of our hierarchies corresponds to a previously studied relaxation (Leung and Matthews in IEEE Trans Inf Theory 61(8):4486, 2015) and positive partial transpose constraints can be added to give a sufficient criterion for the exact convergence at a given level of the hierarchy. To quantify the worst case convergence speed of our sum-of-squares hierarchies, we derive novel quantum de Finetti theorems that allow imposing linear constraints on the approximating state. In particular, we give finite de Finetti theorems for quantum channels, quantifying closeness to the convex hull of product channels as well as closeness to local operations and classical forward communication assisted channels. As a special case this constitutes a finite version of Fuchs-Schack-Scudo’s asymptotic de Finetti theorem for quantum channels. Finally, our proof methods answer a question of Brandão and Harrow (Proceedings of the forty-fourth annual ACM symposium on theory of computing, STOC’12, p 307, 2012) by improving the approximation factor of de Finetti theorems with no symmetry from $$O(d^{k/2})$$ O ( d k / 2 ) to $${\mathrm {poly}}(d,k)$$ poly ( d , k ) , where d denotes local dimension and k the number of copies.
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Mahmoodian, Vahid, Iman Dayarian, Payman Ghasemi Saghand, Yu Zhang, and Hadi Charkhgard. "A Criterion Space Branch-and-Cut Algorithm for Mixed Integer Bilinear Maximum Multiplicative Programs." INFORMS Journal on Computing, January 4, 2022. http://dx.doi.org/10.1287/ijoc.2021.1097.
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This study introduces a branch-and-bound algorithm to solve mixed-integer bilinear maximum multiplicative programs (MIBL-MMPs). This class of optimization problems arises in many applications, such as finding a Nash bargaining solution (Nash social welfare optimization), capacity allocation markets, reliability optimization, etc. The proposed algorithm applies multiobjective optimization principles to solve MIBL-MMPs exploiting a special characteristic in these problems. That is, taking each multiplicative term in the objective function as a dummy objective function, the projection of an optimal solution of MIBL-MMPs is a nondominated point in the space of dummy objectives. Moreover, several enhancements are applied and adjusted to tighten the bounds and improve the performance of the algorithm. The performance of the algorithm is investigated by 400 randomly generated sample instances of MIBL-MMPs. The obtained result is compared against the outputs of the mixed-integer second order cone programming (SOCP) solver in CPLEX and a state-of-the-art algorithm in the literature for this problem. Our analysis on this comparison shows that the proposed algorithm outperforms the fastest existing method, that is, the SOCP solver, by a factor of 6.54 on average. Summary of Contribution: The scope of this paper is defined over a class of mixed-integer programs, the so-called mixed-integer bilinear maximum multiplicative programs (MIBL-MMPs). The importance of MIBL-MMPs is highlighted by the fact that they are encountered in applications, such as Nash bargaining, capacity allocation markets, reliability optimization, etc. The mission of the paper is to introduce a novel and effective criterion space branch-and-cut algorithm to solve MIBL-MMPs by solving a finite number of single-objective mixed-integer linear programs. Starting with an initial set of primal and dual bounds, our proposed approach explores the efficient set of the multiobjective problem counterpart of the MIBL-MMP through a criterion space–based branch-and-cut paradigm and iteratively improves the bounds using a branch-and-bound scheme. The bounds are obtained using novel operations developed based on Chebyshev distance and piecewise McCormick envelopes. An extensive computational study demonstrates the efficacy of the proposed algorithm.
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Goubko, Mikhail, and Alexander Kuznetsov. "Lower bound for the cost of connecting tree with given vertex degree sequence." Journal of Complex Networks 8, no. 2 (August 17, 2019). http://dx.doi.org/10.1093/comnet/cnz031.
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Abstract The optimal connecting network problem generalizes many models of structure optimization known from the literature, including communication and transport network topology design, graph cut and graph clustering, etc. For the case of connecting trees with the given sequence of vertex degrees the cost of the optimal tree is shown to be bounded from below by the solution of a semidefinite optimization program with bilinear matrix inequality constraints, which is reduced to the solution of a series of convex programs with linear matrix inequality constraints. The proposed lower-bound estimate is used to construct several heuristic algorithms and to evaluate their quality on a variety of generated and real-life datasets.
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Zolan, Alexander J., Michael S. Scioletti, David P. Morton, and Alexandra M. Newman. "Decomposing Loosely Coupled Mixed-Integer Programs for Optimal Microgrid Design." INFORMS Journal on Computing, February 8, 2021. http://dx.doi.org/10.1287/ijoc.2020.0955.
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Microgrids are frequently employed in remote regions, in part because access to a larger electric grid is impossible, difficult, or compromises reliability and independence. Although small microgrids often employ spot generation, in which a diesel generator is attached directly to a load, microgrids that combine these individual loads and augment generators with photovoltaic cells and batteries as a distributed energy system are emerging as a safer, less costly alternative. We present a model that seeks the minimum-cost microgrid design and ideal dispatched power to support a small remote site for one year with hourly fidelity under a detailed battery model; this mixed-integer nonlinear program (MINLP) is intractable with commercial solvers but loosely coupled with respect to time. A mixed-integer linear program (MIP) approximates the model, and a partitioning scheme linearizes the bilinear terms. We introduce a novel policy for loosely coupled MIPs in which the system reverts to equivalent conditions at regular time intervals; this separates the problem into subproblems that we solve in parallel. We obtain solutions within 5% of optimality in at most six minutes across 14 MIP instances from the literature and solutions within 5% of optimality to the MINLP instances within 20 minutes.
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Büsing, Christina, Timo Gersing, and Arie M. C. A. Koster. "A branch and bound algorithm for robust binary optimization with budget uncertainty." Mathematical Programming Computation, January 23, 2023. http://dx.doi.org/10.1007/s12532-022-00232-2.
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AbstractSince its introduction in the early 2000s, robust optimization with budget uncertainty has received a lot of attention. This is due to the intuitive construction of the uncertainty sets and the existence of a compact robust reformulation for (mixed-integer) linear programs. However, despite its compactness, the reformulation performs poorly when solving robust integer problems due to its weak linear relaxation. To overcome the problems arising from the weak formulation, we propose a bilinear formulation for robust binary programming, which is as strong as theoretically possible. From this bilinear formulation, we derive strong linear formulations as well as structural properties for robust binary optimization problems, which we use within a tailored branch and bound algorithm. We test our algorithm’s performance together with other approaches from the literature on a diverse set of “robustified” real-world instances from the MIPLIB 2017. Our computational study, which is the first to compare many sophisticated approaches on a broad set of instances, shows that our algorithm outperforms existing approaches by far. Furthermore, we show that the fundamental structural properties proven in this paper can be used to substantially improve the approaches from the literature. This highlights the relevance of our findings, not only for the tested algorithms, but also for future research on robust optimization. To encourage the use of our algorithms for solving robust optimization problems and our instances for benchmarking, we make all materials freely available online.
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Karimi, Roya, Jianqiang Cheng, and Miguel A. Lejeune. "A Framework for Solving Chance-Constrained Linear Matrix Inequality Programs." INFORMS Journal on Computing, October 19, 2020. http://dx.doi.org/10.1287/ijoc.2020.0982.
Full textAbstract:
We propose a novel partial sample average approximation (PSAA) framework to solve the two main types of chance-constrained linear matrix inequality (CCLMI) problems: CCLMI with random technology matrix and CCLMI with random right-hand side. We propose a series of computationally tractable PSAA-based approximations for CCLMI problems, analyze their properties, and derive sufficient conditions that ensure convexity for the two most popular—normal and uniform—continuous distributions. We derive several semidefinite programming PSAA reformulations efficiently solved by off-the-shelf solvers and design a sequential convex approximation method for the PSAA formulations containing bilinear matrix inequalities. The proposed methods can be generalized to other continuous random variables whose cumulative distribution function can be easily computed. We carry out a comprehensive numerical study on three practical CCLMI problems: robust truss topology design, calibration, and robust control. The tests attest to the superiority of the PSAA reformulation and algorithmic framework over the scenario and sample average approximation methods. Summary of Contribution: In line with the mission and scope of IJOC, we study an important type of optimization problems, chance-constrained linear matrix inequality (CCLMI) problems, which require stochastic linear matrix inequality (LMI) constraints to be satisfied with high probability. To solve CCLMI problems, we propose a novel partial sample average approximation (PSAA) framework: (i) develop a series of computationally tractable PSAA-based approximations for CCLMI problems, (ii) analyze their properties, (iii) derive sufficient conditions ensuring convexity, and (iv) design a sequential convex approximation method. We evaluate our proposed method via a comprehensive numerical study on three practical CCLMI problems. The tests attest the superiority of the PSAA reformulation and algorithmic framework over standard benchmarks.
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Jiang, Nan, and Weijun Xie. "ALSO-X and ALSO-X+: Better Convex Approximations for Chance Constrained Programs." Operations Research, February 1, 2022. http://dx.doi.org/10.1287/opre.2021.2225.
Full textAbstract:
In a chance constrained program (CCP), decision makers seek the best decision whose probability of violating the uncertainty constraints is within the prespecified risk level. As a CCP is often nonconvex and is difficult to solve to optimality, much effort has been devoted to developing convex inner approximations for a CCP, among which the conditional value-at-risk (CVaR) has been known to be the best for more than a decade. This paper studies and generalizes the ALSO-X, originally proposed by Ahmed, Luedtke, SOng, and Xie in 2017 , for solving a CCP. We first show that the ALSO-X resembles a bilevel optimization, where the upper-level problem is to find the best objective function value and enforce the feasibility of a CCP for a given decision from the lower-level problem, and the lower-level problem is to minimize the expectation of constraint violations subject to the upper bound of the objective function value provided by the upper-level problem. This interpretation motivates us to prove that when uncertain constraints are convex in the decision variables, ALSO-X always outperforms the CVaR approximation. We further show (i) sufficient conditions under which ALSO-X can recover an optimal solution to a CCP; (ii) an equivalent bilinear programming formulation of a CCP, inspiring us to enhance ALSO-X with a convergent alternating minimization method (ALSO-X+); and (iii) an extension of ALSO-X and ALSO-X+ to distributionally robust chance constrained programs (DRCCPs) under the ∞−Wasserstein ambiguity set. Our numerical study demonstrates the effectiveness of the proposed methods.