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Journal articles on the topic 'Production function (dual and primal)'

Author: Grafiati

Published: 1 July 2022

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1

Paris, Quirino. "Certezze e novitŕ in economia della produzione." QA Rivista dell'Associazione Rossi-Doria, no. 3 (August 2009): 7–22. http://dx.doi.org/10.3280/qu2009-003001.

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- Michele De Benedictis has for some time taken an interest in behavioral models for agricultural entrepreneurs. Often, such models are specified by means of a production function and a cost function with the associated derived demands for inputs. In order to make such models operational in a given empirical setting, the approach in the traditional literature has been to estimate either the production function and the associated first order conditions or the system of derived demand functions for inputs. This paper proposes an encompassing approach which consists in the joint estimation of the production function and the associated first order conditions and the system of derived demand functions. Empirical verification lends support to the hypothesis that full utilization of the available information requires a primal-dual approach, as presented in this paper.EconLit Classification: C600, D210Keywords: Production Function, Cost Function, Primal-Dual Method, Joint EstimationParole chiave: Funzione di produzione, Funzione di costo, Metodo primario-duale, Stima congiunta

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Sugianto, Welly. "OPTIMASI KAPASITAS PRODUKSI UKM DENGAN GOAL PROGRAMMING." JURNAL REKAYASA SISTEM INDUSTRI 5, no. 2 (May 30, 2020): 146. http://dx.doi.org/10.33884/jrsi.v5i2.1911.

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UKM Jovelyn is a small medium enterprise (SME) that engaged in the field of bakery production. Until now, they produce cakes and cookies. They sell products throughout the Batam area which includes (Tiban market, aviari market, mitra market and puja bahari market), shops, school canteens and so on. The SME targets several things such as profit per month, number of hours worked, number of overtime hours, machine utilities, labor utilities and so forth. Until now, the SME has not been able to reach the targets because the UKM has not determined the production amount based on the appropriate calculation. The number of products made is determined only on an intuitive basis. Determination of the amount of production cannot be determined by the usual simplex method because the objective function in the usual simplex method contains a target. Problem solving is done by using goal programming. The results of the calculation analysis show that to achieve the optimal value, the SME must produce coconut root cookies, butter cookies, nastar cookies, snow princess cookies and peanut cookies respectively 11.89 kg, 22.43 kg, 24.96 kg , 1.97kg and 0 kg. Sensitivity analysis is carried out after there are changes in conditions that result in changes in the linear program matrix, so the number of products that must be made also changes which include coconut root cookies as much as 12.8 kg, as much as 16.91 kg of butter cookies, nastar cookies as much as 25.7 and the last is 3.39 kg of nut cookies which in the initial calculation, nut cookies were not produced. The sensitivity analysis is not done by recalculation but rather by modifying the matrix and completing iteration with primal dual.

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Xing, Yumei, and Dong Qiu. "Solving Triangular Intuitionistic Fuzzy Matrix Game by Applying the Accuracy Function Method." Symmetry 11, no. 10 (October 9, 2019): 1258. http://dx.doi.org/10.3390/sym11101258.

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In this paper, the matrix game based on triangular intuitionistic fuzzy payoff is put forward. Then, we get a conclusion that the equilibrium solution of this game model is equivalent to the solution of a pair of the primal–dual single objective intuitionistic fuzzy linear optimization problems ( I F L O P 1 ) and ( I F L O D 1 ) . Furthermore, by applying the accuracy function, which is linear, we transform the primal–dual single objective intuitionistic fuzzy linear optimization problems ( I F L O P 1 ) and ( I F L O D 1 ) into the primal–dual discrete linear optimization problems ( G L O P 1 ) and ( G L O D 1 ) . The above primal–dual pair ( G L O P 1 ) – ( G L O D 1 ) is symmetric in the sense the dual of ( G L O D 1 ) is ( G L O P 1 ) . Thus the primal–dual discrete linear optimization problems ( G L O P 1 ) and ( G L O D 1 ) are called the symmetric primal–dual discrete linear optimization problems. Finally, the technique is illustrated by an example.

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4

Sheu, Ruey-Lin, and Shu-Cherng Fang. "On the relationship of interior-point methods." International Journal of Mathematics and Mathematical Sciences 16, no. 3 (1993): 565–72. http://dx.doi.org/10.1155/s0161171293000699.

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In this paper, we show that the moving directions of the primal-affine scaling method (with logarithmic barrier function), the dual-affine scaling method (with logarithmic barrier function), and the primal-dual interior point method are merely the Newton directions along three different algebraic paths that lead to a solution of the Karush-Kuhn-Tucker conditions of a given linear programming problem. We also derive the missing dual information in the primal-affine scaling method and the missing primal information in the dual-affine scaling method. Basically, the missing information has the same form as the solutions generated by the primal-dual method but with different scaling matrices.

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5

Mundlak, Yair. "Production Function Estimation: Reviving the Primal." Econometrica 64, no. 2 (March 1996): 431. http://dx.doi.org/10.2307/2171790.

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6

Tanikawa, A., and H. Mukai. "New Lagrangian function for nonconvex primal-dual decomposition." Computers & Mathematics with Applications 13, no. 8 (1987): 661–76. http://dx.doi.org/10.1016/0898-1221(87)90039-3.

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7

Huang, Zhiyi, and Anthony Kim. "Welfare maximization with production costs: A primal dual approach." Games and Economic Behavior 118 (November 2019): 648–67. http://dx.doi.org/10.1016/j.geb.2018.03.003.

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8

Kumbhakar, Subal C., and Efthymios G. Tsionas. "Stochastic error specification in primal and dual production systems." Journal of Applied Econometrics 26, no. 2 (June 16, 2009): 270–97. http://dx.doi.org/10.1002/jae.1100.

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9

Xing, Wenxun, Shu-Cherng Fang, Ruey-Lin Sheu, and Liping Zhang. "Canonical Dual Solutions to Quadratic Optimization over One Quadratic Constraint." Asia-Pacific Journal of Operational Research 32, no. 01 (February 2015): 1540007. http://dx.doi.org/10.1142/s0217595915400072.

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A quadratic optimization problem with one nonconvex quadratic constraint is studied using the canonical dual approach. Under the dual Slater's condition, we show that the canonical dual has a smooth concave objective function over a convex feasible domain, and this dual has a finite supremum unless the original quadratic optimization problem is infeasible. This supremum, when it exists, always equals to the minimum value of the primal problem. Moreover, a global minimizer of the primal problem can be provided by a dual-to-primal conversion plus a "boundarification" technique. Application to solving a quadratic programming problem over a ball is included and an error bound estimation is provided.

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10

Ye, Xugang, Shih-Ping Han, and Anhua Lin. "A Note on the Connection Between the Primal-Dual and the A* Algorithm." International Journal of Operations Research and Information Systems 1, no. 1 (January 2010): 73–85. http://dx.doi.org/10.4018/joris.2010101305.

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The primal-dual algorithm for linear programming is very effective for solving network flow problems. For the method to work, an initial feasible solution to the dual is required. In this article, we show that, for the shortest path problem in a positively weighted graph equipped with a consistent heuristic function, the primal-dual algorithm will become the well-known A* algorithm if a special initial feasible solution to the dual is chosen. We also show how the improvements of the dual objective are related to the A* iterations.

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11

Iftimie, Bogdan, Monique Jeanblanc, and Thomas Lim. "Optimization problem under change of regime of interest rate." Stochastics and Dynamics 16, no. 05 (July 15, 2016): 1650015. http://dx.doi.org/10.1142/s0219493716500155.

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In this paper, we study the problem of maximization of the expected value of the sum of the utility of the terminal wealth and the utility of the consumption, in a case where some sudden jumps in the risk-free interest rate create incompleteness. To solve the problem we use the dual approach. We characterize the value function of the dual problem by a BSDE and the duality between the primal and the dual value functions is exploited to study the BSDE associated to the primal problem.

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12

Hasan, M. Babul, and Md Toha. "An Improved Subgradiend Optimization Technique for Solving IPs with Lagrangean Relaxation." Dhaka University Journal of Science 61, no. 2 (November 18, 2013): 135–40. http://dx.doi.org/10.3329/dujs.v61i2.17059.

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The objective of this paper is to improve the subgradient optimization method which is used to solve non-differentiable optimization problems in the Lagrangian dual problem. One of the main drawbacks of the subgradient method is the tuning process to determine the sequence of step-lengths to update successive iterates. In this paper, we propose a modified subgradient optimization method with various step size rules to compute a tuning- free subgradient step-length that is geometrically motivated and algebraically deduced. It is well known that the dual function is a concave function over its domain (regardless of the structure of the cost and constraints of the primal problem), but not necessarily differentiable. We solve the dual problem whenever it is easier to solve than the primal problem with no duality gap. However, even if there is a duality gap the solution of the dual problem provides a lower bound to the primal optimum that can be useful in combinatorial optimization. Numerical examples are illustrated to demonstrate the method. DOI: http://dx.doi.org/10.3329/dujs.v61i2.17059 Dhaka Univ. J. Sci. 61(2): 135-140, 2013 (July)

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13

Liang, Dong, and Wilbert E. Wilhelm. "Dual-ascent and primal heuristics for production-assembly-distribution system design." Naval Research Logistics (NRL) 60, no. 1 (December 20, 2012): 1–18. http://dx.doi.org/10.1002/nav.21515.

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14

EL Ghami, M., and T. Steihaug. "Kernel-function Based Primal-Dual Algorithms forP*(κ) Linear Complementarity Problems." RAIRO - Operations Research 44, no. 3 (July 2010): 185–205. http://dx.doi.org/10.1051/ro/2010014.

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15

Chan, T. H. Hubert, Kevin L. Chang, and Rajiv Raman. "An SDP Primal-Dual Algorithm for Approximating the Lovász-Theta Function." Algorithmica 69, no. 3 (February 13, 2013): 605–18. http://dx.doi.org/10.1007/s00453-013-9756-5.

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Huang, Ming, Li-Ping Pang, Xi-Jun Liang, and Zun-Quan Xia. "The Space Decomposition Theory for a Class of Semi-Infinite Maximum Eigenvalue Optimizations." Abstract and Applied Analysis 2014 (2014): 1–12. http://dx.doi.org/10.1155/2014/845017.

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We study optimization problems involving eigenvalues of symmetric matrices. We present a nonsmooth optimization technique for a class of nonsmooth functions which are semi-infinite maxima of eigenvalue functions. Our strategy uses generalized gradients and𝒰𝒱space decomposition techniques suited for the norm and other nonsmooth performance criteria. For the class of max-functions, which possesses the so-called primal-dual gradient structure, we compute smooth trajectories along which certain second-order expansions can be obtained. We also give the first- and second-order derivatives of primal-dual function in the space of decision variablesRmunder some assumptions.

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17

Lu, Fang, and Chun-Rong Chen. "Notes on Lipschitz Properties of Nonlinear Scalarization Functions with Applications." Abstract and Applied Analysis 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/792364.

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Various kinds of nonlinear scalarization functions play important roles in vector optimization. Among them, the one commonly known as the Gerstewitz function is good at scalarizing. In linear normed spaces, the globally Lipschitz property of such function is deduced via primal and dual spaces approaches, respectively. The equivalence of both expressions for globally Lipschitz constants obtained by primal and dual spaces approaches is established. In particular, when the ordering cone is polyhedral, the expression for calculating Lipschitz constant is given. As direct applications of the Lipschitz property, several sufficient conditions for Hölder continuity of both single-valued and set-valued solution mappings to parametric vector equilibrium problems are obtained using the nonlinear scalarization approach.

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18

Cho, Gyeong-Mi, Y. Y. Cho, and Y. H. Lee. "A primal-dual interior-point algorithm based on a new kernel function." ANZIAM Journal 51 (May 3, 2011): 476. http://dx.doi.org/10.21914/anziamj.v51i0.1724.

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CHO, G. M., Y. Y. CHO, and Y. H. LEE. "A PRIMAL-DUAL INTERIOR-POINT ALGORITHM BASED ON A NEW KERNEL FUNCTION." ANZIAM Journal 51, no. 4 (April 2010): 476–91. http://dx.doi.org/10.1017/s1446181110000908.

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AbstractWe propose a new primal-dual interior-point algorithm based on a new kernel function for linear optimization problems. New search directions and proximity functions are proposed based on the kernel function. We show that the new algorithm has $\mathcal {O}(\sqrt {n} \log n \log ({n}/{\epsilon }))$ and $\mathcal {O}(\sqrt {n}\log ({n}/{\epsilon }))$ iteration bounds for large-update and small-update methods, respectively, which are currently the best known bounds for such methods.

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20

Bai, Yan-Qin, Jing Zhang, Peng-Fei Ma, and Lian-Sheng Zhang. "A self-concordant exponential kernel function for primal–dual interior-point algorithm." Optimization 63, no. 6 (October 18, 2013): 931–53. http://dx.doi.org/10.1080/02331934.2013.845777.

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21

EL Ghami, M., and C. Roos. "Generic Primal-dual Interior Point Methods Based on a New Kernel Function." RAIRO - Operations Research 42, no. 2 (April 2008): 199–213. http://dx.doi.org/10.1051/ro:2008009.

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22

Zhao, Dequan, and Mingwang Zhang. "Kernel function-based primal-dual interior-point methods for symmetric cones optimization." Wuhan University Journal of Natural Sciences 19, no. 6 (November 12, 2014): 461–68. http://dx.doi.org/10.1007/s11859-014-1040-2.

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23

Ito, S., C. T. Kelley, and E. W. Sachs. "Inexact primal-dual interior point iteration for linear programs in function spaces." Computational Optimization and Applications 4, no. 3 (July 1995): 189–201. http://dx.doi.org/10.1007/bf01300870.

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24

Nesterov, Yu. "Complexity bounds for primal-dual methods minimizing the model of objective function." Mathematical Programming 171, no. 1-2 (August 21, 2017): 311–30. http://dx.doi.org/10.1007/s10107-017-1188-6.

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25

Kaur, Arshpreet, and MaheshKumar Sharma. "Higher order symmetric duality for multiobjective fractional programming problems over cones." Yugoslav Journal of Operations Research, no. 00 (2021): 12. http://dx.doi.org/10.2298/yjor200615012k.

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This article studies a pair of higher order nondifferentiable symmetric fractional programming problem over cones. First, higher order cone convex function is introduced. Then using the properties of this function, duality results are set up, which give the legitimacy of the pair of primal dual symmetric model.

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26

Postolache, Mihai. "Duality for Multitime Multiobjective Ratio Variational Problems on First Order Jet Bundle." Abstract and Applied Analysis 2012 (2012): 1–18. http://dx.doi.org/10.1155/2012/589694.

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We consider a new class of multitime multiobjective variational problems of minimizing a vector of quotients of functionals of curvilinear integral type. Based on the efficiency conditions for multitime multiobjective ratio variational problems, we introduce a ratio dual of generalized Mond-Weir-Zalmai type, and under some assumptions of generalized convexity, duality theorems are stated. We prove our weak duality theorem for efficient solutions, showing that the value of the objective function of the primal cannot exceed the value of the dual. Direct and converse duality theorems are stated, underlying the connections between the values of the objective functions of the primal and dual programs. As special cases, duality results of Mond-Weir-Zalmai type for a multitime multiobjective variational problem are obtained. This work further develops our studies in (Pitea and Postolache (2011)).

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27

Hong, Mingyi, Tsung-Hui Chang, Xiangfeng Wang, Meisam Razaviyayn, Shiqian Ma, and Zhi-Quan Luo. "A Block Successive Upper-Bound Minimization Method of Multipliers for Linearly Constrained Convex Optimization." Mathematics of Operations Research 45, no. 3 (August 2020): 833–61. http://dx.doi.org/10.1287/moor.2019.1010.

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Consider the problem of minimizing the sum of a smooth convex function and a separable nonsmooth convex function subject to linear coupling constraints. Problems of this form arise in many contemporary applications, including signal processing, wireless networking, and smart grid provisioning. Motivated by the huge size of these applications, we propose a new class of first-order primal–dual algorithms called the block successive upper-bound minimization method of multipliers (BSUM-M) to solve this family of problems. The BSUM-M updates the primal variable blocks successively by minimizing locally tight upper bounds of the augmented Lagrangian of the original problem, followed by a gradient-type update for the dual variable in closed form. We show that under certain regularity conditions, and when the primal block variables are updated in either a deterministic or a random fashion, the BSUM-M converges to a point in the set of optimal solutions. Moreover, in the absence of linear constraints and under similar conditions as in the previous result, we show that the randomized BSUM-M (which reduces to the randomized block successive upper-bound minimization method) converges at an asymptotically linear rate without relying on strong convexity.

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Orea Sánchez, Luis, and Antonio Álvarez Pinilla. "Eficiencia técnica en pesquerias multiespecie: Una aproximación primal." Economía Agraria y Recursos Naturales 2, no. 1 (October 23, 2011): 5. http://dx.doi.org/10.7201/earn.2002.01.01.

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The objective of this paper is to study, following a primal approach, the technical efficiency of a sample of boats which catch hake in Asturias. In this activity the catches of species different from hake are important. The multiproduct nature of this activity raises different modelling alternatives. In this paper we compare the results obtained in the estimation of an aggregate production function, a multiproduct production function, and a distance function. The three models are estimated using the within-groups estimator. After eliminating the influence of time invariant variables, the efficiency indexes are calculated in a second stage using the individual fixed effects. The empirical analysis uses a panel data set of eleven boats in 1999.

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Izmailov, A. F., M. V. Solodov, and E. I. Uskov. "Globalizing Stabilized Sequential Quadratic Programming Method by Smooth Primal-Dual Exact Penalty Function." Journal of Optimization Theory and Applications 169, no. 1 (February 11, 2016): 148–78. http://dx.doi.org/10.1007/s10957-016-0889-y.

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30

Duffin, R. J., D. F. Karney, and E. Z. Prisman. "Apex duality for constrained optimization." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 28, no. 1 (July 1986): 134–46. http://dx.doi.org/10.1017/s0334270000005233.

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In this paper, we develop a duality theory for the Apex dual in the case of primal constraints. As suggested by Duffin in [4], the objective function in this framework is a weighted average of the Legendre-Lagrangian function evaluated at key points. We show that whenever this new dual is feasible there is no duality gap for this dual, and moreover, no duality gap for both the Lagrangian and Wolfe duals too. We conclude with an outline of an algorithm to solve constrained minimization problems in the Apex framework.

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Yuan, Jing, Juan Shi, and Xue-Cheng Tai. "A Convex and Exact Approach to Discrete Constrained TV-L1 Image Approximation." East Asian Journal on Applied Mathematics 1, no. 2 (May 2011): 172–86. http://dx.doi.org/10.4208/eajam.220310.181110a.

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AbstractWe study the TV-L1 image approximation model from primal and dual perspective, based on a proposed equivalent convex formulations. More specifically, we apply a convex TV-L1 based approach to globally solve the discrete constrained optimization problem of image approximation, where the unknown image function u(x) ∈ {f1,…,fn}, ∀x ∈ Ω. We show that the TV-L1 formulation does provide an exact convex relaxation model to the non-convex optimization problem considered. This result greatly extends recent studies of Chan et al., from the simplest binary constrained case to the general gray-value constrained case, through the proposed rounding scheme. In addition, we construct a fast multiplier-based algorithm based on the proposed primal-dual model, which properly avoids variability of the concerning TV-L1 energy function. Numerical experiments validate the theoretical results and show that the proposed algorithm is reliable and effective.

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Scott, C. H., T. R. Jefferson, and E. Sirri. "On duality for convex minimization with nested maxima." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 26, no. 4 (April 1985): 517–22. http://dx.doi.org/10.1017/s0334270000004690.

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AbstractIn this paper, we consider convex programs with linear constraints where the objective function involves nested maxima of linear functions as well as a convex function. A dual program is constructed which has interpretational significance and may be easier to solve than the primal formulation. A numerical example is given to illustrate the method.

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Kermani, Ali A., Christian B. Macdonald, Roja Gundepudi, and Randy B. Stockbridge. "Guanidinium export is the primal function of SMR family transporters." Proceedings of the National Academy of Sciences 115, no. 12 (March 5, 2018): 3060–65. http://dx.doi.org/10.1073/pnas.1719187115.

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The small multidrug resistance (SMR) family of membrane proteins is prominent because of its rare dual topology architecture, simplicity, and small size. Its best studied member, EmrE, is an important model system in several fields related to membrane protein biology, from evolution to mechanism. But despite decades of work on these multidrug transporters, the native function of the SMR family has remained a mystery, and many highly similar SMR homologs do not transport drugs at all. Here we establish that representative SMR proteins, selected from each of the major clades in the phylogeny, function as guanidinium ion exporters. Drug-exporting SMRs are all clustered in a single minority clade. Using membrane transport experiments, we show that these guanidinium exporters, which we term Gdx, are very selective for guanidinium and strictly and stoichiometrically couple its export with the import of two protons. These findings draw important mechanistic distinctions with the notably promiscuous and weakly coupled drug exporters like EmrE.

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De Marchi, Alberto. "On a primal-dual Newton proximal method for convex quadratic programs." Computational Optimization and Applications 81, no. 2 (January 6, 2022): 369–95. http://dx.doi.org/10.1007/s10589-021-00342-y.

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AbstractThis paper introduces QPDO, a primal-dual method for convex quadratic programs which builds upon and weaves together the proximal point algorithm and a damped semismooth Newton method. The outer proximal regularization yields a numerically stable method, and we interpret the proximal operator as the unconstrained minimization of the primal-dual proximal augmented Lagrangian function. This allows the inner Newton scheme to exploit sparse symmetric linear solvers and multi-rank factorization updates. Moreover, the linear systems are always solvable independently from the problem data and exact linesearch can be performed. The proposed method can handle degenerate problems, provides a mechanism for infeasibility detection, and can exploit warm starting, while requiring only convexity. We present details of our open-source C implementation and report on numerical results against state-of-the-art solvers. QPDO proves to be a simple, robust, and efficient numerical method for convex quadratic programming.

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Breslaw, J. A., and J. B. Smith. "Des observations empiriques encourageantes pour la théorie dualiste." Articles 59, no. 2 (July 21, 2009): 230–39. http://dx.doi.org/10.7202/601214ar.

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De récents résultats empiriques suggèrent que les caractéristiques estimées des technologies de production dépendent du modèle postulé (primal ou dual). Dans cet article nous nous intéressons à ce problème. Nous concluons que de différences significatives n’existent pas en ce qui concerne les données de Bell Canada.

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Tchelepi, Hamdi A., Patrick Jenny, Seong Hee Lee, and Christian Wolfsteiner. "Adaptive Multiscale Finite-Volume Framework for Reservoir Simulation." SPE Journal 12, no. 02 (June 1, 2007): 188–95. http://dx.doi.org/10.2118/93395-pa.

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Summary A multiscale finite-volume (MSFV) framework for reservoir simulation is described. This adaptive MSFV formulation is locally conservative and yields accurate results of both flow and transport in large-scale highly heterogeneous reservoir models. IMPES and sequential implicit formulations are described. The algorithms are sensitive to the specific characteristics of flow (i.e., pressure and total velocity) and transport (i.e., saturation). To compute the fine-scale flow field, two sets of basis functions - dual and primal - are constructed. The dual basis functions, which are associated with the dual coarse grid, are used to calculate the coarse scale transmissibilities. The fine-scale pressure field is computed from the coarse grid pressure via superposition of the dual basis functions. Having a locally conservative fine scale velocity field is essential for accurate solution of the saturation equations (i.e., transport). The primal basis functions, which are associated with the primal coarse grid, are constructed for that purpose. The dual basis functions serve as boundary conditions to the primal basis functions. To resolve the fine-scale flow field in and around wells, a special well basis function is devised. As with the other basis functions, we ensure that the support for the well basis is local. Our MSFV framework is designed for adaptive computation of both flow and transport in the course of a simulation run. Adaptive computation of the flow field is based on the time change of the total mobility field, which triggers the selective updating of basis functions. The key to achieving scalable (efficient for large problems) adaptive computation of flow and transport is the use of high fidelity basis functions with local support. We demonstrate the robustness and computational efficiency of the MSFV simulator using a variety of large heterogeneous reservoir models, including the SPE 10 comparative solution problem.

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Alain, Guinet. "A primal-dual approach for capacity-constrained production planning with variable and fixed costs." Computers & Industrial Engineering 37, no. 1-2 (October 1999): 93–96. http://dx.doi.org/10.1016/s0360-8352(99)00030-3.

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Wang, G. Q., Y. Q. Bai, and C. Roos. "Primal-Dual Interior-Point Algorithms for Semidefinite Optimization Based on a Simple Kernel Function." Journal of Mathematical Modelling and Algorithms 4, no. 4 (October 26, 2005): 409–33. http://dx.doi.org/10.1007/s10852-005-3561-3.

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Chai, Yanfei. "Robust strong duality for nonconvex optimization problem under data uncertainty in constraint." AIMS Mathematics 6, no. 11 (2021): 12321–38. http://dx.doi.org/10.3934/math.2021713.

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<abstract><p>This paper deals with the robust strong duality for nonconvex optimization problem with the data uncertainty in constraint. A new weak conjugate function which is abstract convex, is introduced and three kinds of robust dual problems are constructed to the primal optimization problem by employing this weak conjugate function: the robust augmented Lagrange dual, the robust weak Fenchel dual and the robust weak Fenchel-Lagrange dual problem. Characterizations of inequality (1.1) according to robust abstract perturbation weak conjugate duality are established by using the abstract convexity. The results are used to obtain robust strong duality between noncovex uncertain optimization problem and its robust dual problems mentioned above, the optimality conditions for this noncovex uncertain optimization problem are also investigated.</p></abstract>

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Popov, Sergei P., and Darya V. Maksakova. "One approach to the study of gas pricing based on gas supply systems modelling (the case of Northeast Asia)." E3S Web of Conferences 114 (2019): 02004. http://dx.doi.org/10.1051/e3sconf/201911402004.

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The article deals with the approach to gas pricing analysis based on the use of optimization models of gas supply systems. The object of the study is the Northeast Asian gas market. The model of the excessive gas supply system in Northeast Asia is described. The primal problem of the model is to minimize the sum of gas production and transportation costs under the infrastructure constraints. The solutions to the primal problem are the volumes of gas produced in each production point and transported via each route. The solutions to the dual problem (dual variables or shadow prices) are node prices in the points of gas supply system, the producers’ rent and the transporters’ rent. It is highlighted that the dual analysis plays an important role. It allows evaluating price relations between the points of gas supply system, identifying export routs characterized by the highest rent, evaluating the competitiveness of suppliers in the different scenarios of technological development, energy policy and market environment. The analytical capacities of the dual analysis are illustrated by the study of the impact of “unconventional” gas development in the importing countries on the Northeast Asian gas market environment. When the costs of unconventional gas production rise, gas trade patterns change, more competitive players enter the market, and gas prices in all consumption points as well as producers’ rents increase. It is concluded that if importers seek to lower import dependency while keeping the same price level, they have to lower the costs of unconventional gas production by technological development and/or to subsidize the industry to make it more competitive.

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41

Jiang, Xin, and Lieven Vandenberghe. "Bregman primal–dual first-order method and application to sparse semidefinite programming." Computational Optimization and Applications 81, no. 1 (December 4, 2021): 127–59. http://dx.doi.org/10.1007/s10589-021-00339-7.

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AbstractWe present a new variant of the Chambolle–Pock primal–dual algorithm with Bregman distances, analyze its convergence, and apply it to the centering problem in sparse semidefinite programming. The novelty in the method is a line search procedure for selecting suitable step sizes. The line search obviates the need for estimating the norm of the constraint matrix and the strong convexity constant of the Bregman kernel. As an application, we discuss the centering problem in large-scale semidefinite programming with sparse coefficient matrices. The logarithmic barrier function for the cone of positive semidefinite completable sparse matrices is used as the distance-generating kernel. For this distance, the complexity of evaluating the Bregman proximal operator is shown to be roughly proportional to the cost of a sparse Cholesky factorization. This is much cheaper than the standard proximal operator with Euclidean distances, which requires an eigenvalue decomposition.

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Cai, Xinzhong, Lin Wu, Yujing Yue, Minmin Li, and Guoqiang Wang. "Kernel-function-based primal-dual interior-point methods for convex quadratic optimization over symmetric cone." Journal of Inequalities and Applications 2014, no. 1 (2014): 308. http://dx.doi.org/10.1186/1029-242x-2014-308.

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Bai, Y. Q., C. Roos, and M. El Ghami. "A primal‐dual interior-point method for linear optimization based on a new proximity function." Optimization Methods and Software 17, no. 6 (January 2002): 985–1008. http://dx.doi.org/10.1080/1055678021000090024.

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Yamashita, Hiroshi, and Hiroshi Yabe. "An Interior Point Method with a Primal-Dual Quadratic Barrier Penalty Function for Nonlinear Optimization." SIAM Journal on Optimization 14, no. 2 (January 2003): 479–99. http://dx.doi.org/10.1137/s1052623499355533.

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Baptista, E. C., E. A. Belati, V. A. Sousa, and G. R. M. Da Costa. "Primal-Dual Logarithmic Barrier and Augmented Lagrangian Function to the Loss Minimization in Power Systems." Electric Power Components and Systems 34, no. 7 (June 2006): 775–84. http://dx.doi.org/10.1080/15325000500488602.

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Wang, Guoqiang, and Detong Zhu. "A unified kernel function approach to primal-dual interior-point algorithms for convex quadratic SDO." Numerical Algorithms 57, no. 4 (January 6, 2011): 537–58. http://dx.doi.org/10.1007/s11075-010-9444-3.

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Cheng, Z. Y., and J. E. Mitchell. "A primal-dual interior-point method for linear programming based on a weighted barrier function." Journal of Optimization Theory and Applications 87, no. 2 (November 1995): 301–21. http://dx.doi.org/10.1007/bf02192566.

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Guminov, S. V., Yu E. Nesterov, P. E. Dvurechensky, and A. V. Gasnikov. "Primal-dual accelerated gradient descent with line search for convex and nonconvex optimization problems." Доклады Академии наук 485, no. 1 (May 22, 2019): 15–18. http://dx.doi.org/10.31857/s0869-5652485115-18.

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In this paper a new variant of accelerated gradient descent is proposed. The proposed method does not require any information about the objective function, uses exact line search for the practical accelerations of convergence, converges according to the well-known lower bounds for both convex and non-convex objective functions and possesses primal-dual properties. We also provide a universal version of said method, which converges according to the known lower bounds for both smooth and non-smooth problems.

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Loubna, Guerra, and Achache Mohamed. "A Parametric Kernel Function Generating the best Known Iteration Bound for Large-Update Methods for CQSDO." Statistics, Optimization & Information Computing 8, no. 4 (September 24, 2020): 876–89. http://dx.doi.org/10.19139/soic-2310-5070-842.

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In this paper, we propose a large-update primal-dual interior point algorithm for convex quadratic semidefiniteoptimization (CQSDO) based on a new parametric kernel function. This kernel function is a parameterized version of the kernel function introduced by M.W. Zhang (Acta Mathematica Sinica. 28: 2313-2328, 2012) for CQSDO. The investigation according to it generating the best known iteration bound O for large-update methods. Thus improves the iteration bound obtained by Zhang for large-update methods. Finally, we present few numerical results to show the efficiency of the proposed algorithm.

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Boudjellal, Nawel, Hayet Roumili, and Djamel Benterki. "Complexity analysis of interior point methods for convex quadratic programming based on a parameterized Kernel function." Boletim da Sociedade Paranaense de Matemática 40 (February 2, 2022): 1–16. http://dx.doi.org/10.5269/bspm.47772.

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The kernel functions play an important role in the amelioration of the computational complexity of algorithms. In this paper, we present a primal-dual interior-point algorithm for solving convex quadratic programming based on a new parametric kernel function. The proposed kernel function is not logarithmic and not self-regular. We analysis a large and small-update versions which are based on a new kernel function. We obtain the best known iteration bound for large-update methods, which improves signicantly the so far obtained complexity results. Thisresult is the rst to reach this goal.

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