Artykuły w czasopismach: „SDP optimization”

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MEVISSEN, MARTIN, i MASAKAZU KOJIMA. "SDP RELAXATIONS FOR QUADRATIC OPTIMIZATION PROBLEMS DERIVED FROM POLYNOMIAL OPTIMIZATION PROBLEMS". Asia-Pacific Journal of Operational Research 27, nr 01 (luty 2010): 15–38. http://dx.doi.org/10.1142/s0217595910002533.

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Based on the convergent sequence of SDP relaxations for a multivariate polynomial optimization problem (POP) by Lasserre (2006), Waki et al. (2006) constructed a sequence of sparse SDP relaxations to solve sparse POPs efficiently. Nevertheless, the size of the sparse SDP relaxation is the major obstacle in order to solve POPs of higher degree. This paper proposes an approach to transform general POPs to quadratic optimization problems (QOPs), which allows to reduce the size of the SDP relaxation substantially. We introduce different heuristics resulting in equivalent QOPs and show how sparsity of a POP is maintained under the transformation procedure. As the most important issue, we discuss how to increase the quality of the SDP relaxation for a QOP. Moreover, we increase the accuracy of the solution of the SDP relaxation by applying additional local optimization techniques. Finally, we demonstrate the high potential of this approach through numerical results for large scale POPs of higher degree.

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Liu, Yiyuan, Baoguo Li i Yizhou Yao. "Radar-Embedded Communication Waveform Design Based on Parameter Optimization". Journal of Physics: Conference Series 2404, nr 1 (1.12.2022): 012032. http://dx.doi.org/10.1088/1742-6596/2404/1/012032.

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Abstract Radar-embedded communication (REC) is a low probability of intercept (LPI) communication method that enables radar and communication to share the spectrum. Covert communication is accomplished by embedding low-power communication waveforms in high-power radar backscatter echoes. This research, by optimizing the eigenvalue matrix power exponent a of the shaped dominant projection (SDP) waveform, proposes an SDP waveform with variable eigenvalue matrix power exponent, namely SDP-a waveform. Then, the reliability of waveform communication and LPI performance are theoretically analyzed by processing gain. Finally, the simulation experiments are carried out with SDP-0.25, SDP-0.5, and SDP-0.75 waveforms as examples. The experimental results are consistent with the theoretical analysis results, indicating that the optimization of the eigenvalue matrix power exponent can meet the performance requirements of different aspects.

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Metzlaff, Tobias. "Symmetry Adapted Bases for Trigonometric Optimization". ACM Communications in Computer Algebra 57, nr 3 (wrzesień 2023): 137–40. http://dx.doi.org/10.1145/3637529.3637535.

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We present an algorithm to compute the global minimum of a trigonometric polynomial, when it is invariant under the exponential action of a Weyl group. This is based on a common relaxation technique that leads to a semi-definite program (SDP). It is then shown how to exploit the invariance in order to reduce the number of variables of the SDP and to simplify its structure significantly. This approach complements the one that was proposed as a poster at the recent ISSAC 2022 conference [HMMR22] and later extended to [HMMR23]. In the previous work, we first used the invariance of the objective function to obtain a classical polynomial optimization problem on the orbit space and subsequently relaxed the problem to an SDP. In the present work, we first apply the relaxation and then exploit symmetry. We show that the Weyl group action is induced by an orthogonal representation and describe its isotypic decomposition.

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Hu, En-Liang, i Bo Wang. "A new optimization in SDP-based learning". Neurocomputing 365 (listopad 2019): 10–20. http://dx.doi.org/10.1016/j.neucom.2019.06.058.

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Hu, Haijiang, Shaojing Song i Fengdeng Zhang. "FIR to FIR Model Reduction with Linear Group Delay in Passband by SDP Optimization". Journal of Electrical and Computer Engineering 2020 (20.02.2020): 1–7. http://dx.doi.org/10.1155/2020/4503706.

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Filter model reduction is an important optimization method in digital signal processing. A method of FIR to FIR model reduction using SDP optimization is proposed in this paper. At first, we use SDP to design an original FIR filter. Then we name a general K-order FIR digital filter H1z−1 with coefficient values equal to the first K + 1 filter coefficient values of H0z−1. Finally, we design a new general K-order FIR digital filter H2z−1 connected in parallel with H1z−1 using SDP optimization. The experiment results show this method has good performance on the magnitude error and the linear phase in passband. Therefore, this method can be used in the field of digital signal processing.

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KANNO, Y., M. OHSAKI i N. KATOH. "SEQUENTIAL SEMIDEFINITE PROGRAMMING FOR OPTIMIZATION OF FRAMED STRUCTURES UNDER MULTIMODAL BUCKLING CONSTRAINTS". International Journal of Structural Stability and Dynamics 01, nr 04 (grudzień 2001): 585–602. http://dx.doi.org/10.1142/s0219455401000305.

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An algorithm based on Semi-Definite Programming (SDP) formulation is proposed for optimum design of structures for specified linear buckling load factors. Optimal trusses and frames are computed by using the primal-dual interior-point method based on SDP scheme. It is well known that optimizing structures under buckling constraints is difficult because of the non-differentiability of buckling load factors for the case of multimodal solutions. The examples studied indicate that optimum designs with multiple buckling load factors can be found with no difficulty by successively solving the SDP problems.

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Gil-González, Walter, Alexander Molina-Cabrera, Oscar Danilo Montoya i Luis Fernando Grisales-Noreña. "An MI-SDP Model for Optimal Location and Sizing of Distributed Generators in DC Grids That Guarantees the Global Optimum". Applied Sciences 10, nr 21 (30.10.2020): 7681. http://dx.doi.org/10.3390/app10217681.

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This paper deals with a classical problem in power system analysis regarding the optimal location and sizing of distributed generators (DGs) in direct current (DC) distribution networks using the mathematical optimization. This optimization problem is divided into two sub-problems as follows: the optimal location of DGs is a problem, with those with a binary structure being the first sub-problem; and the optimal sizing of DGs with a nonlinear programming (NLP) structure is the second sub-problem. These problems originate from a general mixed-integer nonlinear programming model (MINLP), which corresponds to an NP-hard optimization problem. It is not possible to provide the global optimum with conventional programming methods. A mixed-integer semidefinite programming (MI-SDP) model is proposed to address this problem, where the binary part is solved via the branch and bound (B&B) methods and the NLP part is solved via convex optimization (i.e., SDP). The main advantage of the proposed MI-SDP model is the possibility of guaranteeing a global optimum solution if each of the nodes in the B&B search is convex, as is ensured by the SDP method. Numerical validations in two test feeders composed of 21 and 69 nodes demonstrate that in all of these problems, the optimal global solution is reached by the MI-SDP approach, compared to the classical metaheuristic and hybrid programming models reported in the literature. All the simulations have been carried out using the MATLAB software with the CVX tool and the Mosek solver.

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Ren, Fangyu, Huotao Gao, Lijuan Yang i Sang Zhou. "Distributed Multistatic Sky-Wave Over-the-Horizon Radar’s Positioning Algorithm for the Marine Target". International Journal of Antennas and Propagation 2021 (27.10.2021): 1–7. http://dx.doi.org/10.1155/2021/1028784.

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This paper establishes a distributed multistatic sky-wave over-the-horizon radar (DMOTHR) model and proposes a semidefinite relaxation positioning (SDP) algorithm to locate marine ship targets. In the DMOTHR, it is difficult to locate the target due to the complexity of the signal path propagation. Therefore, this paper uses the ionosphere as the reflector to convert the propagation path from a polyline to a straight line for establishing the model, and then the SDP algorithm will be used to transform a highly nonlinear positioning optimization problem into a convex optimization problem. Finally, it is concluded through the simulations that the SDP algorithm can obtain better positioning accuracy under a certain Doppler frequency error and ionospheric measurement error.

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Nandyala, Raja Thejaswini, i Muthupandi Gandhi. "High uncertainty aware localization and error optimization of mobile nodes for wireless sensor networks". IAES International Journal of Artificial Intelligence (IJ-AI) 12, nr 4 (1.12.2023): 2022. http://dx.doi.org/10.11591/ijai.v12.i4.pp2022-2032.

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The localization of mobile sensor nodes in a wireless sensor network (WSN) is a key research area for the speedy development of wireless communication and microelectronics. The localization of mobile sensor nodes massively depends upon the received signal strength (RSS). Recently, the least squared relative error (LSRE) measurements are optimized using traditional semidefinite programming (SDP) and the location of the mobile sensor nodes was determined using the previous localization methods like least squared relative error and semidefinite programming (LSRE-SDP), and approximate nonlinear least squares and semidefinite programming (ANLS-SDP). Therefore, in this work, a novel high uncertainty aware-localization error correction and optimization (HUA-LECO) model is employed to minimize the aforementioned problems regarding the localization of mobile sensor nodes and enhance the performance efficiency of root mean square error (RMSE) results. Here, the position of target mobile sensor nodes is evaluated based on the gathered measurements while discarding faulty data. Here, an iterative weight updation approach is utilized to perform localization based on Monte Carlo simulations. Simulation results show significant improvement in terms of RMSE results in comparison with traditional LSRE-SDP and ANLS-SDP methods under high uncertainty.

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Guolei, Tang, Zhou Huicheng i Li Ningning. "Reservoir optimization model incorporating inflow forecasts with various lead times as hydrologic state variables". Journal of Hydroinformatics 12, nr 3 (24.11.2009): 292–302. http://dx.doi.org/10.2166/hydro.2009.088.

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This paper presents two Stochastic Dynamic Programming models (SDP) to investigate the potential value of inflow forecasts with various lead times in hydropower generation. The proposed SDP frameworks generate hydropower operating policies for the Ertan hydropower station, China. The objective function maximizes the total hydropower generation with the firm capacity committed for the system. The two proposed SDP-derived operating policies are simulated using historical inflows, as well as inflow forecasts with various lead times. Four performance indicators are chosen to assist in selecting the best reservoir operating policy: mean annual hydropower production, Nash–Sutcliffe sufficiency score, reliability and vulnerability. Performances of the proposed SDP-derived policies are compared with those of other existing policies. The simulation results demonstrate that including inflow forecasts with various lead times is beneficial to the Ertan hydropower generation, and the chosen operating policy cannot only yield higher hydropower production, but also produces reasonable storage hydrographs effectively.

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Lasserre, Jean B. "Convergent SDP‐Relaxations in Polynomial Optimization with Sparsity". SIAM Journal on Optimization 17, nr 3 (styczeń 2006): 822–43. http://dx.doi.org/10.1137/05064504x.

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Nie, Jiawang. "An exact Jacobian SDP relaxation for polynomial optimization". Mathematical Programming 137, nr 1-2 (22.09.2011): 225–55. http://dx.doi.org/10.1007/s10107-011-0489-4.

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Cifuentes, Diego, Corey Harris i Bernd Sturmfels. "The geometry of SDP-exactness in quadratic optimization". Mathematical Programming 182, nr 1-2 (15.05.2019): 399–428. http://dx.doi.org/10.1007/s10107-019-01399-8.

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Kuang, Xiaolong, Bissan Ghaddar, Joe Naoum-Sawaya i Luis F. Zuluaga. "Alternative SDP and SOCP approximations for polynomial optimization". EURO Journal on Computational Optimization 7, nr 2 (13.08.2018): 153–75. http://dx.doi.org/10.1007/s13675-018-0101-2.

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Riener, Cordian, Thorsten Theobald, Lina Jansson Andrén i Jean B. Lasserre. "Exploiting Symmetries in SDP-Relaxations for Polynomial Optimization". Mathematics of Operations Research 38, nr 1 (luty 2013): 122–41. http://dx.doi.org/10.1287/moor.1120.0558.

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Kolumbán, Sándor, i Istvan Vajk. "Identification Aspects of SDP Based Polynomial Optimization Relaxations*". IFAC Proceedings Volumes 45, nr 16 (lipiec 2012): 1209–14. http://dx.doi.org/10.3182/20120711-3-be-2027.00227.

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Lasserre, Jean-Bernard, i Victor Magron. "In SDP Relaxations, Inaccurate Solvers Do Robust Optimization". SIAM Journal on Optimization 29, nr 3 (styczeń 2019): 2128–45. http://dx.doi.org/10.1137/18m1225677.

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Kang, Jonggu, Sunjae Kwon, Duksan Ryu i Jongmoon Baik. "HASPO: Harmony Search-Based Parameter Optimization for Just-in-Time Software Defect Prediction in Maritime Software". Applied Sciences 11, nr 5 (24.02.2021): 2002. http://dx.doi.org/10.3390/app11052002.

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Software is playing the most important role in recent vehicle innovations, and consequently the amount of software has rapidly grown in recent decades. The safety-critical nature of ships, one sort of vehicle, makes software quality assurance (SQA) a fundamental prerequisite. Just-in-time software defect prediction (JIT-SDP) aims to conduct software defect prediction (SDP) on commit-level code changes to achieve effective SQA resource allocation. The first case study of SDP in the maritime domain reported feasible prediction performance. However, we still consider that the prediction model has room for improvement since the parameters of the model are not optimized yet. Harmony search (HS) is a widely used music-inspired meta-heuristic optimization algorithm. In this article, we demonstrated that JIT-SDP can produce better performance of prediction by applying HS-based parameter optimization with balanced fitness value. Using two real-world datasets from the maritime software project, we obtained an optimized model that meets the performance criterion beyond the baseline of a previous case study throughout various defect to non-defect class imbalance ratio of datasets. Experiments with open source software also showed better recall for all datasets despite the fact that we considered balance as a performance index. HS-based parameter optimized JIT-SDP can be applied to the maritime domain software with a high class imbalance ratio. Finally, we expect that our research can be extended to improve the performance of JIT-SDP not only in maritime domain software but also in open source software.

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Lee, Jon, i Leo Liberti. "On an SDP relaxation for kissing number". Optimization Letters 14, nr 2 (1.02.2018): 417–22. http://dx.doi.org/10.1007/s11590-018-1239-9.

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Kobayashi, Kazuhiro, Kazuhide Nakata i Masakazu Kojima. "A conversion of an SDP having free variables into the standard form SDP". Computational Optimization and Applications 36, nr 2-3 (21.02.2007): 289–307. http://dx.doi.org/10.1007/s10589-006-9002-z.

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Anvari, Sedigheh, S. Jamshid Mousavi i Saeed Morid. "Sampling/stochastic dynamic programming for optimal operation of multi-purpose reservoirs using artificial neural network-based ensemble streamﬂow predictions". Journal of Hydroinformatics 16, nr 4 (18.12.2013): 907–21. http://dx.doi.org/10.2166/hydro.2013.236.

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Due to limited water resources and the increasing demand for agricultural products, it is significantly important to operate surface water reservoirs optimally, especially those located in arid and semi-arid regions. This paper investigates uncertainty-based optimal operation of a multi-purpose water reservoir system by using four optimization models. The models include dynamic programming (DP), stochastic DP (SDP) with inflow classification (SDP/Class), SDP with inflow scenarios (SDP/Scenario), and sampling SDP (SSDP) with historical scenarios (SSDP/Hist). The performance of the models was tested in Zayandeh-Rud Reservoir system in Iran by evaluating how their release policies perform in a simulation phase. While the SDP approaches were better than the DP approach, the SSDP/Hist model outperformed the other SDP models. We also assessed the effect of ensemble streamflow predictions (ESPs) that were generated by artificial neural networks on the performance of SSDP/Hist. Application of the models to the Zayandeh-Rud case study demonstrated that SSDP in combination with ESPs and the K-means technique, which was used to cluster a large number of ESPs, could be a promising approach for real-time reservoir operation.

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Shahbazian, Reza, i Seyed Ali Ghorashi. "Localization of Distributed Wireless Sensor Networks using Two Sage SDP Optimization". International Journal of Electrical and Computer Engineering (IJECE) 7, nr 3 (1.06.2017): 1255. http://dx.doi.org/10.11591/ijece.v7i3.pp1255-1261.

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A wireless sensor network (WSN) may comprise a large distributed set of low cost, low power sensing nodes. In many applications, the location of sensors is a necessity to evaluate the sensed data and it is not energy and cost efficient to equip all sensors with global positioning systems such as GPS. In this paper, we focus on the localization of sensors in a WSN by solving an optimization problem. In WSN localization, some sensors (called anchors) are aware of their location. Then, the distance measurements between sensors and anchors locations are used to localize the whole sensors in the network. WSN localization is a non-convex optimization problem, however, relaxation techniques such as semi-definite programming (SDP) are used to relax the optimization. To solve the optimization problem, all constraints should be considered simultaneously and the solution complexity order is O(n2) where n is the number of sensors. The complexity of SDP prevents solving large size problems. Therefore, it would be beneficial to reduce the problem size in large and distributed WSNs. In this paper, we propose a two stage optimization to reduce the solution time, while provide better accuracy compared with original SDP method. We first select some sensors that have the maximum connection with anchors and perform the SDP localization. Then, we select some of these sensors as virtual anchors. By adding the virtual anchors, we add more reference points and decrease the number of constraints. We propose an algorithm to select and add virtual anchors so that the total solution complexity and time decrease considerably, while improving the localization accuracy.

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Javanmard, Adel, Andrea Montanari i Federico Ricci-Tersenghi. "Phase transitions in semidefinite relaxations". Proceedings of the National Academy of Sciences 113, nr 16 (21.03.2016): E2218—E2223. http://dx.doi.org/10.1073/pnas.1523097113.

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Statistical inference problems arising within signal processing, data mining, and machine learning naturally give rise to hard combinatorial optimization problems. These problems become intractable when the dimensionality of the data is large, as is often the case for modern datasets. A popular idea is to construct convex relaxations of these combinatorial problems, which can be solved efficiently for large-scale datasets. Semidefinite programming (SDP) relaxations are among the most powerful methods in this family and are surprisingly well suited for a broad range of problems where data take the form of matrices or graphs. It has been observed several times that when the statistical noise is small enough, SDP relaxations correctly detect the underlying combinatorial structures. In this paper we develop asymptotic predictions for several detection thresholds, as well as for the estimation error above these thresholds. We study some classical SDP relaxations for statistical problems motivated by graph synchronization and community detection in networks. We map these optimization problems to statistical mechanics models with vector spins and use nonrigorous techniques from statistical mechanics to characterize the corresponding phase transitions. Our results clarify the effectiveness of SDP relaxations in solving high-dimensional statistical problems.

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Jeyakumar, V., G. Li i J. Vicente-Pérez. "Robust SOS-convex polynomial optimization problems: exact SDP relaxations". Optimization Letters 9, nr 1 (26.02.2014): 1–18. http://dx.doi.org/10.1007/s11590-014-0732-z.

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G.S L. Brandão, Fernando, Richard Kueng i Daniel Stilck França. "Faster quantum and classical SDP approximations for quadratic binary optimization". Quantum 6 (20.01.2022): 625. http://dx.doi.org/10.22331/q-2022-01-20-625.

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We give a quantum speedup for solving the canonical semidefinite programming relaxation for binary quadratic optimization. This class of relaxations for combinatorial optimization has so far eluded quantum speedups. Our methods combine ideas from quantum Gibbs sampling and matrix exponent updates. A de-quantization of the algorithm also leads to a faster classical solver. For generic instances, our quantum solver gives a nearly quadratic speedup over state-of-the-art algorithms. Such instances include approximating the ground state of spin glasses and MaxCut on Erdös-Rényi graphs. We also provide an efficient randomized rounding procedure that converts approximately optimal SDP solutions into approximations of the original quadratic optimization problem.

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Gally, Tristan, Christopher M. Gehb, Philip Kolvenbach, Anja Kuttich, Marc E. Pfetsch i Stefan Ulbrich. "Robust Truss Topology Design with Beam Elements via Mixed Integer Nonlinear Semidefinite Programming". Applied Mechanics and Materials 807 (listopad 2015): 229–38. http://dx.doi.org/10.4028/www.scientific.net/amm.807.229.

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In this article, we propose a nonlinear semidefinite program (SDP) for the robust trusstopology design (TTD) problem with beam elements. Starting from the semidefinite formulation ofthe robust TTD problem we derive a stiffness matrix that can model rigid connections between beams.Since the stiffness matrix depends nonlinearly on the cross-sectional areas of the beams, this leads toa nonlinear SDP. We present numerical results using a sequential SDP approach and compare them toresults obtained via a general method for robust PDE-constrained optimization applied to the equationsof linear elasticity. Furthermore, we present two mixed integer semidefinite programs (MISDP), onefor the optimal choice of connecting elements, which is nonlinear, and one for the correspondingproblem with discrete cross-sectional areas.

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Luo, Weiwen, Xulei Chen, Mingyang Qin, Kai Guo, Jie Ling, Fengwei Gu i Zhichao Hu. "Design and Experiment of Uniform Seed Device for Wide-Width Seeder of Wheat after Rice Stubble". Agriculture 13, nr 11 (20.11.2023): 2173. http://dx.doi.org/10.3390/agriculture13112173.

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When wide-width sowing wheat after rice stubble (WRS) in a rice-wheat rotation area, there is a problem of poor uniform of seed distribution. To solve the problem, this study designed the seed distribution plate (SDP) structure and optimized its critical structure parameters. Firstly, combined with the operating principles of the wide-width seeder and the agricultural standards for WRS, the main structural parameters affecting seed movement were determined by a theoretical analysis of seed grain dynamics and SDP structure. Secondly, the operational performance of six different structures of SDP under different structural parameters was compared using discrete element simulation technology. The structure of SDP most suitable for WRS wide-width seeding and the value ranges of key structural parameters that have a significant impact on the coefficient of the variation of seed lateral uniformity (CVLU) were determined. Finally, the pattern and mechanism of the influence of key structural parameters of SDP on the CVLU were analyzed. The optimum parameter combination was obtained and a field validation test was conducted on this. The results showed that the anti-arc ridge and arc bottom structure (S6) is more suitable for the agronomy standards of WRS wide-width seeding. The chord length of ridge, installation inclination, angle between the chord and tangent of the end of ridge line (ACT), span, and bottom curve radius are determined as the key structural parameters affecting the CVLU, and there is a lower CVLU (42.8%) when the ACT is 13°. The primary and secondary order of the influence of each factor on CVLU is the chord length of the ridge, span, installation inclination, and bottom curve radius. The corresponding parameter values after optimization are 140 mm, 40°, 75 mm and 50 mm, respectively. A field test was conducted on the SDP after optimizing parameters, and the CVLU was 30.27%, which was significantly lower than the CVLU before optimization.

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Yamada, Keigo, Yasuo Sasaki, Takayuki Nagata, Kumi Nakai, Daisuke Tsubakino i Taku Nonomura. "Efficient Sensor Node Selection for Observability Gramian Optimization". Sensors 23, nr 13 (27.06.2023): 5961. http://dx.doi.org/10.3390/s23135961.

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Optimization approaches that determine sensitive sensor nodes in a large-scale, linear time-invariant, and discrete-time dynamical system are examined under the assumption of independent and identically distributed measurement noise. This study offers two novel selection algorithms, namely an approximate convex relaxation method with the Newton method and a gradient greedy method, and confirms the performance of the selection methods, including a convex relaxation method with semidefinite programming (SDP) and a pure greedy optimization method proposed in the previous studies. The matrix determinant of the observability Gramian was employed for the evaluations of the sensor subsets, while its gradient and Hessian were derived for the proposed methods. In the demonstration using numerical and real-world examples, the proposed approximate greedy method showed superiority in the run time when the sensor numbers were roughly the same as the dimensions of the latent system. The relaxation method with SDP is confirmed to be the most reasonable approach for a system with randomly generated matrices of higher dimensions. However, the degradation of the optimization results was also confirmed in the case of real-world datasets, while the pure greedy selection obtained the most stable optimization results.

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Nie, Jiawang, i Li Wang. "Regularization Methods for SDP Relaxations in Large-Scale Polynomial Optimization". SIAM Journal on Optimization 22, nr 2 (styczeń 2012): 408–28. http://dx.doi.org/10.1137/110825844.

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Kočvara, Michal, i Michael Stingl. "Solving nonconvex SDP problems of structural optimization with stability control". Optimization Methods and Software 19, nr 5 (październik 2004): 595–609. http://dx.doi.org/10.1080/10556780410001682844.

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Haijema, René, Nico van Dijk, Jan van der Wal i Cees Smit Sibinga. "Blood platelet production with breaks: optimization by SDP and simulation". International Journal of Production Economics 121, nr 2 (październik 2009): 464–73. http://dx.doi.org/10.1016/j.ijpe.2006.11.026.

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Ahmadi, Amir Ali, i Bachir El Khadir. "Time-Varying Semidefinite Programs". Mathematics of Operations Research 46, nr 3 (sierpień 2021): 1054–80. http://dx.doi.org/10.1287/moor.2020.1117.

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We study time-varying semidefinite programs (TV-SDPs), which are semidefinite programs whose data (and solutions) are functions of time. Our focus is on the setting where the data vary polynomially with time. We show that under a strict feasibility assumption, restricting the solutions to also be polynomial functions of time does not change the optimal value of the TV-SDP. Moreover, by using a Positivstellensatz (positive locus theorem) on univariate polynomial matrices, we show that the best polynomial solution of a given degree to a TV-SDP can be found by solving a semidefinite program of tractable size. We also provide a sequence of dual problems that can be cast as SDPs and that give upper bounds on the optimal value of a TV-SDP (in maximization form). We prove that under a boundedness assumption, this sequence of upper bounds converges to the optimal value of the TV-SDP. Under the same assumption, we also show that the optimal value of the TV-SDP is attained. We demonstrate the efficacy of our algorithms on a maximum-flow problem with time-varying edge capacities, a wireless coverage problem with time-varying coverage requirements, and on biobjective semidefinite optimization where the goal is to approximate the Pareto curve in one shot.

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Wiegele, Angelika, i Shudian Zhao. "SDP-based bounds for graph partition via extended ADMM". Computational Optimization and Applications 82, nr 1 (17.03.2022): 251–91. http://dx.doi.org/10.1007/s10589-022-00355-1.

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AbstractWe study two NP-complete graph partition problems, k-equipartition problems and graph partition problems with knapsack constraints (GPKC). We introduce tight SDP relaxations with nonnegativity constraints to get lower bounds, the SDP relaxations are solved by an extended alternating direction method of multipliers (ADMM). In this way, we obtain high quality lower bounds for k-equipartition on large instances up to $$n =1000$$ n = 1000 vertices within as few as 5 min and for GPKC problems up to $$n=500$$ n = 500 vertices within as little as 1 h. On the other hand, interior point methods fail to solve instances from $$n=300$$ n = 300 due to memory requirements. We also design heuristics to generate upper bounds from the SDP solutions, giving us tighter upper bounds than other methods proposed in the literature with low computational expense.

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Ni, Zhitong, Andrew Jian Zhang, Ren-Ping Liu i Kai Yang. "Doubly Constrained Waveform Optimization for Integrated Sensing and Communications". Sensors 23, nr 13 (28.06.2023): 5988. http://dx.doi.org/10.3390/s23135988.

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This paper investigates threshold-constrained joint waveform optimization for an integrated sensing and communication (ISAC) system. Unlike existing studies, we employ mutual information (MI) and sum rate (SR) as sensing and communication metrics, respectively, and optimize the waveform under constraints to both metrics simultaneously. This provides significant flexibility in meeting system performance. We formulate three different optimization problems that constrain the radar performance only, the communication performance only, and the ISAC performance, respectively. New techniques are developed to solve the original problems, which are NP-hard and cannot be directly solved by conventional semi-definite programming (SDP) techniques. Novel gradient descent methods are developed to solve the first two problems. For the third non-convex optimization problem, we transform it into a convex problem and solve it via convex toolboxes. We also disclose the connections between three optimizations using numerical results. Finally, simulation results are provided and validate the proposed optimization solutions.

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Adib, Arash, Iman Ahmadeanfar, Meysam Salarijazi, Mojtaba Labibzadeh i Mohammad Vaghefi. "Optimization of Released Water from the Dez Dam for Supply of Water Demands in the Downstream of Dam". Applied Mechanics and Materials 147 (grudzień 2011): 187–90. http://dx.doi.org/10.4028/www.scientific.net/amm.147.187.

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For supplying of water demands in the downstream of dams, optimization of released water from reservoir of dam is necessary. Released water from reservoir is related to discharge of inflow to reservoir, volume of evaporation from reservoir and storage of reservoir. Water demands are includes of drinkable water and agricultural water demand. If released water from reservoir is less than water demands in a month, this month will be a defeat. After a defeat, reservoir must return to normal condition in order to supply of water demands in next months. For minimize the number of defeats and maximize return ability of reservoir to normal condition, a suitable method must be applied for optimization of volume of released water from reservoir. In this research, two optimum methods (SDP method and GA method) were applied for minimize the number of defeats and maximize return ability of reservoir to normal condition. For this purpose, reservoir of the Dez dam was considered in this research. The Dez dam locates in the south-west of Iran on the Dez River. At the end, it is observed that GA method can minimize the number of defeats and maximize return ability of reservoir to normal condition better than SDP method. But SDP method can minimize damage function better than GA method.

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Campbell, Joy, i Javier Polo. "PSIX-5 Spray Dried Plasma Increases Protein and Meat Inclusion in Extruded Dog Kibbles". Journal of Animal Science 101, Supplement_3 (6.11.2023): 445–46. http://dx.doi.org/10.1093/jas/skad281.529.

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Abstract A common goal for pet food manufacturers extruding dry kibbles is to increase meat inclusion and protein content in both grain and grain free formulas. When extruding high meat formulas, variation of moisture and fat of the incoming raw meat ingredients adds to the complexity of producing consistent quality kibbles meeting all specifications. Spray dried plasma (SDP) is a consistent high protein ingredient commonly utilized in wet pet food for water binding and fat emulsification characteristics and in dry kibble extrusion with meat meals and other dry ingredients to produce quality kibbles. Thus, the objective of two studies was to evaluate if meat inclusion levels could be increased in extruded formulas with the use of SDP. Tests were done at the Wenger technology testing center to evaluate combinations of SDP levels ranging from 2.5 to 20% with meat level feed rates ranging from 25 to 50%. The ability to produce kibbles was conducted utilizing both grain free and grain formulations. Processing conditions were monitored on the various formulations during production along with kibble outcome measurements such as ability to extrude, solids, protein, and durability. In the first study, extrusion of grain free formulations with 0% SDP resulted in meat inclusion limit at 35% feed rate. Addition of 5, 10, and 15% SDP in grain free formulas increased protein content of the extruded kibble but meat inclusion was limited at 35% feed rate. However, use of 20% SDP in grain free formulas allowed for greater inclusion of meat from 35% and up to 45% feed rate while maintaining kibble quality and increasing protein. Extrusion of a grain formulation with 0% SDP also resulted in limits of 35% feed rate of meat inclusion. Addition of 2.5, 5, 10, or 20% SDP to grain formulations allowed for meat inclusion feed rate to be increased up to 50% depending on levels of SDP used, and protein was increased in all combinations. The second study was completed to evaluate a longer run extrusion measuring ability to extrude, cook, and durability. Grain free formulas were run at 35% feed rate of meat with 5, 10, or 20% SDP and maintained cook and durability. Grain formulas were run at 45% feed rate of meat with 2.5, 5, and 10% SDP and maintained durability with further optimization of cook needed. Overall, SDP included in the formulation allows for greater feed rate of meat inclusion and maintain or increase protein and durability in the dry kibble. Thus, depending on target meat inclusion feed rates or protein levels, SDP may be used during the extrusion process to produce dry kibbles with high meat inclusion.

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Khurma, Ruba Abu, Hamad Alsawalqah, Ibrahim Aljarah, Mohamed Abd Elaziz i Robertas Damaševičius. "An Enhanced Evolutionary Software Defect Prediction Method Using Island Moth Flame Optimization". Mathematics 9, nr 15 (22.07.2021): 1722. http://dx.doi.org/10.3390/math9151722.

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Software defect prediction (SDP) is crucial in the early stages of defect-free software development before testing operations take place. Effective SDP can help test managers locate defects and defect-prone software modules. This facilitates the allocation of limited software quality assurance resources optimally and economically. Feature selection (FS) is a complicated problem with a polynomial time complexity. For a dataset with N features, the complete search space has 2N feature subsets, which means that the algorithm needs an exponential running time to traverse all these feature subsets. Swarm intelligence algorithms have shown impressive performance in mitigating the FS problem and reducing the running time. The moth flame optimization (MFO) algorithm is a well-known swarm intelligence algorithm that has been used widely and proven its capability in solving various optimization problems. An efficient binary variant of MFO (BMFO) is proposed in this paper by using the island BMFO (IsBMFO) model. IsBMFO divides the solutions in the population into a set of sub-populations named islands. Each island is treated independently using a variant of BMFO. To increase the diversification capability of the algorithm, a migration step is performed after a specific number of iterations to exchange the solutions between islands. Twenty-one public software datasets are used for evaluating the proposed method. The results of the experiments show that FS using IsBMFO improves the classification results. IsBMFO followed by support vector machine (SVM) classification is the best model for the SDP problem over other compared models, with an average G-mean of 78%.

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Delipetrev, Blagoj, Andreja Jonoski i Dimitri P. Solomatine. "A novel nested stochastic dynamic programming (nSDP) and nested reinforcement learning (nRL) algorithm for multipurpose reservoir optimization". Journal of Hydroinformatics 19, nr 1 (17.09.2016): 47–61. http://dx.doi.org/10.2166/hydro.2016.243.

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In this article we present two novel multipurpose reservoir optimization algorithms named nested stochastic dynamic programming (nSDP) and nested reinforcement learning (nRL). Both algorithms are built as a combination of two algorithms; in the nSDP case it is (1) stochastic dynamic programming (SDP) and (2) nested optimal allocation algorithm (nOAA) and in the nRL case it is (1) reinforcement learning (RL) and (2) nOAA. The nOAA is implemented with linear and non-linear optimization. The main novel idea is to include a nOAA at each SDP and RL state transition, that decreases starting problem dimension and alleviates curse of dimensionality. Both nSDP and nRL can solve multi-objective optimization problems without significant computational expenses and algorithm complexity and can handle dense and irregular variable discretization. The two algorithms were coded in Java as a prototype application and on the Knezevo reservoir, located in the Republic of Macedonia. The nSDP and nRL optimal reservoir policies were compared with nested dynamic programming policies, and overall conclusion is that nRL is more powerful, but significantly more complex than nSDP.

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Pang, Bin, Jiaxun Liang, Han Liu, Jiahao Dong, Zhenli Xu i Xin Zhao. "Intelligent Bearing Fault Diagnosis Based on Multivariate Symmetrized Dot Pattern and LEG Transformer". Machines 10, nr 7 (7.07.2022): 550. http://dx.doi.org/10.3390/machines10070550.

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Deep learning based on vibration signal image representation has proven to be effective for the intelligent fault diagnosis of bearings. However, previous studies have focused primarily on dealing with single-channel vibration signal processing, which cannot guarantee the integrity of fault feature information. To obtain more abundant fault feature information, this paper proposes a multivariate vibration data image representation method, named the multivariate symmetrized dot pattern (M-SDP), by combining multivariate variational mode decomposition (MVMD) with symmetrized dot pattern (SDP). In M-SDP, the vibration signals of multiple sensors are simultaneously decomposed by MVMD to obtain the dominant subcomponents with physical meanings. Subsequently, the dominant subcomponents are mapped to different angles of the SDP image to generate the M-SDP image. Finally, the parameters of M-SDP are automatically determined based on the normalized cross-correlation coefficient (NCC) to maximize the difference between different bearing states. Moreover, to improve the diagnosis accuracy and model generalization performance, this paper introduces the local-to-global (LG) attention block and locally enhanced positional encoding (LePE) mechanism into a Swin Transformer to propose the LEG Transformer method. Then, a novel intelligent bearing fault diagnosis method based on M-SDP and the LEG Transformer is developed. The proposed method is validated with two experimental datasets and compared with some other methods. The experimental results indicate that the M-SDP method has improved diagnostic accuracy and stability compared with the original SDP, and the proposed LEG Transformer outperforms the typical Swin Transformer in recognition rate and convergence speed.

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Lourenço, Bruno F., Masakazu Muramatsu i Takashi Tsuchiya. "Solving SDP completely with an interior point oracle". Optimization Methods and Software 36, nr 2-3 (28.01.2021): 425–71. http://dx.doi.org/10.1080/10556788.2020.1850720.

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Campos, Juan S., i Panos Parpas. "A Multigrid Approach to SDP Relaxations of Sparse Polynomial Optimization Problems". SIAM Journal on Optimization 28, nr 1 (styczeń 2018): 1–29. http://dx.doi.org/10.1137/16m1109060.

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Faber, B. A., i J. R. Stedinger. "Reservoir optimization using sampling SDP with ensemble streamflow prediction (ESP) forecasts". Journal of Hydrology 249, nr 1-4 (sierpień 2001): 113–33. http://dx.doi.org/10.1016/s0022-1694(01)00419-x.

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de Carli Silva, Marcel K., i Levent Tunçel. "Strict Complementarity in Semidefinite Optimization with Elliptopes Including the MaxCut SDP". SIAM Journal on Optimization 29, nr 4 (styczeń 2019): 2650–76. http://dx.doi.org/10.1137/18m1193657.

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Buchheim, Christoph, Maribel Montenegro i Angelika Wiegele. "SDP-based branch-and-bound for non-convex quadratic integer optimization". Journal of Global Optimization 73, nr 3 (29.10.2018): 485–514. http://dx.doi.org/10.1007/s10898-018-0717-z.

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Nishimura, Ryoichi, Shunsuke Hayashi i Masao Fukushima. "SDP reformulation for robust optimization problems based on nonconvex QP duality". Computational Optimization and Applications 55, nr 1 (1.12.2012): 21–47. http://dx.doi.org/10.1007/s10589-012-9520-9.

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Tian, Junyang, i Hua Wei. "Global optimization for the OPF problem via two-degree SDP method". IEEJ Transactions on Electrical and Electronic Engineering 10, nr 1 (18.12.2014): 109–11. http://dx.doi.org/10.1002/tee.22068.

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Mendoza-Ramírez, Rosalva, Rodolfo Silva, Ramón Domínguez-Mora, Eduardo Juan-Diego i Eliseo Carrizosa-Elizondo. "Comparison of Two Convergence Criterion in the Optimization Process Using a Recursive Method in a Multi-Reservoir System". Water 14, nr 19 (21.09.2022): 2952. http://dx.doi.org/10.3390/w14192952.

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Stochastic dynamic programming (SDP) is an optimization technique used in the operation of reservoirs for many years. However, being an iterative method requiring considerable computational time, it is important to establish adequate convergence criterion for its most effective use. Based on two previous studies for the optimization of operations in one of the most important multi-reservoir systems in Mexico, this work uses SDP, centred on the interest in the convergence criterion used in the optimization process. In the first trial, following the recommendations in the literature consulted, the difference in the absolute value of two consecutive iterations was taken and compared against a set tolerance value and a discount factor. In the second trial, it was decided to take the squared difference of the two consecutive iterations. In each of the trials, the computational time taken to obtain the optimal operating policy was quantified, along with whether the optimal operating policy was obtained by meeting the convergence criterion or by reaching the maximum number of iterations. With each optimization policy, the operation of the system under study was simulated and four variables were taken as evaluators of the system behaviour. The results showed few differences in the two operation policies but notable differences in the computation time used in the optimization process, as well as in the fulfilment of the convergence criterion.

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Yalçın, Baturalp, Ziye Ma, Javad Lavaei i Somayeh Sojoudi. "Semidefinite Programming versus Burer-Monteiro Factorization for Matrix Sensing". Proceedings of the AAAI Conference on Artificial Intelligence 37, nr 9 (26.06.2023): 10702–10. http://dx.doi.org/10.1609/aaai.v37i9.26270.

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Many fundamental low-rank optimization problems, such as matrix completion, phase retrieval, and robust PCA, can be formulated as the matrix sensing problem. Two main approaches for solving matrix sensing are based on semidefinite programming (SDP) and Burer-Monteiro (B-M) factorization. The former suffers from high computational and space complexities, whereas the latter may return a spurious solution due to the non-convexity of the problem. The existing theoretical guarantees for the success of these methods have led to similar conservative conditions, which may wrongly imply that these methods have comparable performances. In this paper, we shed light on some major differences between these two methods. First, we present a class of structured matrix completion problems for which the B-M methods fail with an overwhelming probability, while the SDP method works correctly. Second, we identify a class of highly sparse matrix completion problems for which the B-M method works and the SDP method fails. Third, we prove that although the B-M method exhibits the same performance independent of the rank of the unknown solution, the success of the SDP method is correlated to the rank of the solution and improves as the rank increases. Unlike the existing literature that has mainly focused on those instances of matrix sensing for which both SDP and B-M work, this paper offers the first result on the unique merit of each method over the alternative approach.

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Amrit, Anand, i Leifur Leifsson. "Applications of surrogate-assisted and multi-fidelity multi-objective optimization algorithms to simulation-based aerodynamic design". Engineering Computations 37, nr 2 (9.08.2019): 430–57. http://dx.doi.org/10.1108/ec-12-2018-0553.

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Purpose The purpose of this work is to apply and compare surrogate-assisted and multi-fidelity, multi-objective optimization (MOO) algorithms to simulation-based aerodynamic design exploration. Design/methodology/approach The three algorithms for multi-objective aerodynamic optimization compared in this work are the combination of evolutionary algorithms, design space reduction and surrogate models, the multi-fidelity point-by-point Pareto set identification and the multi-fidelity sequential domain patching (SDP) Pareto set identification. The algorithms are applied to three cases, namely, an analytical test case, the design of transonic airfoil shapes and the design of subsonic wing shapes, and are evaluated based on the resulting best possible trade-offs and the computational overhead. Findings The results show that all three algorithms yield comparable best possible trade-offs for all the test cases. For the aerodynamic test cases, the multi-fidelity Pareto set identification algorithms outperform the surrogate-assisted evolutionary algorithm by up to 50 per cent in terms of cost. Furthermore, the point-by-point algorithm is around 27 per cent more efficient than the SDP algorithm. Originality/value The novelty of this work includes the first applications of the SDP algorithm to multi-fidelity aerodynamic design exploration, the first comparison of these multi-fidelity MOO algorithms and new results of a complex simulation-based multi-objective aerodynamic design of subsonic wing shapes involving two conflicting criteria, several nonlinear constraints and over ten design variables.

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Pan, Feng, Hanfei Zhang, Xuebao Li, Moyu Zhang i Yang Ji. "Achieving optimal trade-off for student dropout prediction with multi-objective reinforcement learning". PeerJ Computer Science 10 (30.04.2024): e2034. http://dx.doi.org/10.7717/peerj-cs.2034.

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Student dropout prediction (SDP) in educational research has gained prominence for its role in analyzing student learning behaviors through time series models. Traditional methods often focus singularly on either prediction accuracy or earliness, leading to sub-optimal interventions for at-risk students. This issue underlines the necessity for methods that effectively manage the trade-off between accuracy and earliness. Recognizing the limitations of existing methods, this study introduces a novel approach leveraging multi-objective reinforcement learning (MORL) to optimize the trade-off between prediction accuracy and earliness in SDP tasks. By framing SDP as a partial sequence classification problem, we model it through a multiple-objective Markov decision process (MOMDP), incorporating a vectorized reward function that maintains the distinctiveness of each objective, thereby preventing information loss and enabling more nuanced optimization strategies. Furthermore, we introduce an advanced envelope Q-learning technique to foster a comprehensive exploration of the solution space, aiming to identify Pareto-optimal strategies that accommodate a broader spectrum of preferences. The efficacy of our model has been rigorously validated through comprehensive evaluations on real-world MOOC datasets. These evaluations have demonstrated our model’s superiority, outperforming existing methods in achieving optimal trade-off between accuracy and earliness, thus marking a significant advancement in the field of SDP.

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