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Journal articles on the topic 'Generalized Nash equilibrium problems'

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Author: Grafiati

Published: 10 March 2023

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1

Facchinei, Francisco, and Christian Kanzow. "Generalized Nash Equilibrium Problems." Annals of Operations Research 175, no. 1 (November 1, 2009): 177–211. http://dx.doi.org/10.1007/s10479-009-0653-x.

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2

Facchinei, Francisco, and Christian Kanzow. "Generalized Nash equilibrium problems." 4OR 5, no. 3 (September 13, 2007): 173–210. http://dx.doi.org/10.1007/s10288-007-0054-4.

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3

Nasri, Mostafa, and Wilfredo Sosa. "Equilibrium problems and generalized Nash games." Optimization 60, no. 8-9 (August 2011): 1161–70. http://dx.doi.org/10.1080/02331934.2010.527341.

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4

Singh, Shipra, Aviv Gibali, and Simeon Reich. "Multi-Time Generalized Nash Equilibria with Dynamic Flow Applications." Mathematics 9, no. 14 (July 14, 2021): 1658. http://dx.doi.org/10.3390/math9141658.

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We propose a multi-time generalized Nash equilibrium problem and prove its equivalence with a multi-time quasi-variational inequality problem. Then, we establish the existence of equilibria. Furthermore, we demonstrate that our multi-time generalized Nash equilibrium problem can be applied to solving traffic network problems, the aim of which is to minimize the traffic cost of each route and to solving a river basin pollution problem. Moreover, we also study the proposed multi-time generalized Nash equilibrium problem as a projected dynamical system and numerically illustrate our theoretical results.

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5

Facchinei, Francisco, Andreas Fischer, and Veronica Piccialli. "Generalized Nash equilibrium problems and Newton methods." Mathematical Programming 117, no. 1-2 (July 19, 2007): 163–94. http://dx.doi.org/10.1007/s10107-007-0160-2.

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6

Dreves, Axel, and Nathan Sudermann-Merx. "Solving linear generalized Nash equilibrium problems numerically." Optimization Methods and Software 31, no. 5 (April 14, 2016): 1036–63. http://dx.doi.org/10.1080/10556788.2016.1165676.

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7

YANG, ZHE. "Existence of solutions for a system of quasi-variational relation problems and some applications." Carpathian Journal of Mathematics 31, no. 1 (2015): 135–42. http://dx.doi.org/10.37193/cjm.2015.01.16.

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In this paper, we study the existence of solutions for a new class of systems of quasi-variational relation problems on different domains. As applications, we obtain existence theorems of solutions for systems of quasi-variational inclusions, systems of quasi-equilibrium problems, systems of generalized maximal element problems, systems of generalized KKM problems and systems of generalized quasi-Nash equilibrium problems on different domains. The results of this paper improve and generalize several known results on variational relation problems.

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8

Dreves, Axel. "An algorithm for equilibrium selection in generalized Nash equilibrium problems." Computational Optimization and Applications 73, no. 3 (March 7, 2019): 821–37. http://dx.doi.org/10.1007/s10589-019-00086-w.

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9

Fischer, Andreas, Markus Herrich, and Klaus Schönefeld. "GENERALIZED NASH EQUILIBRIUM PROBLEMS - RECENT ADVANCES AND CHALLENGES." Pesquisa Operacional 34, no. 3 (December 2014): 521–58. http://dx.doi.org/10.1590/0101-7438.2014.034.03.0521.

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10

Yuan, Yanhong, Hongwei Zhang, and Liwei Zhang. "A penalty method for generalized Nash equilibrium problems." Journal of Industrial & Management Optimization 8, no. 1 (2012): 51–65. http://dx.doi.org/10.3934/jimo.2012.8.51.

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11

Yu, Chung-Kai, Mihaela van der Schaar, and Ali H. Sayed. "Distributed Learning for Stochastic Generalized Nash Equilibrium Problems." IEEE Transactions on Signal Processing 65, no. 15 (August 1, 2017): 3893–908. http://dx.doi.org/10.1109/tsp.2017.2695451.

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12

Panicucci, Barbara, Massimo Pappalardo, and Mauro Passacantando. "On solving generalized Nash equilibrium problems via optimization." Optimization Letters 3, no. 3 (March 24, 2009): 419–35. http://dx.doi.org/10.1007/s11590-009-0122-0.

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13

Shan, Shu-qiang, Yu Han, and Nan-jing Huang. "Upper Semicontinuity of Solution Mappings to Parametric Generalized Vector Quasiequilibrium Problems." Journal of Function Spaces 2015 (2015): 1–6. http://dx.doi.org/10.1155/2015/764187.

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We establish the upper semicontinuity of solution mappings for a class of parametric generalized vector quasiequilibrium problems. As applications, we obtain the upper semicontinuity of solution mappings to several problems, such as parametric optimization problem, parametric saddle point problem, parametric Nash equilibria problem, parametric variational inequality, and parametric equilibrium problem.

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14

Couellan, Nicolas. "A note on supervised classification and Nash-equilibrium problems." RAIRO - Operations Research 51, no. 2 (February 27, 2017): 329–41. http://dx.doi.org/10.1051/ro/2016024.

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In this note, we investigate connections between supervised classification and (Generalized) Nash equilibrium problems (NEP & GNEP). For the specific case of support vector machines (SVM), we exploit the geometric properties of class separation in the dual space to formulate a non-cooperative game. NEP and Generalized NEP formulations are proposed for both binary and multi-class SVM problems.

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15

Hou, Jian, and Liwei Zhang. "A barrier function method for generalized Nash equilibrium problems." Journal of Industrial & Management Optimization 10, no. 4 (2014): 1091–108. http://dx.doi.org/10.3934/jimo.2014.10.1091.

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16

Dreves, Axel. "Computing all solutions of linear generalized Nash equilibrium problems." Mathematical Methods of Operations Research 85, no. 2 (October 7, 2016): 207–21. http://dx.doi.org/10.1007/s00186-016-0562-0.

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17

e Oliveira, Hime Aguiar, and Antonio Petraglia. "Solving generalized Nash equilibrium problems through stochastic global optimization." Applied Soft Computing 39 (February 2016): 21–35. http://dx.doi.org/10.1016/j.asoc.2015.10.058.

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18

Harms, Nadja, Christian Kanzow, and Oliver Stein. "On differentiability properties of player convex generalized Nash equilibrium problems." Optimization 64, no. 2 (January 23, 2013): 365–88. http://dx.doi.org/10.1080/02331934.2012.752822.

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19

Facchinei, Francisco, and Christian Kanzow. "Penalty Methods for the Solution of Generalized Nash Equilibrium Problems." SIAM Journal on Optimization 20, no. 5 (January 2010): 2228–53. http://dx.doi.org/10.1137/090749499.

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20

Facchinei, Francisco, and Lorenzo Lampariello. "Partial penalization for the solution of generalized Nash equilibrium problems." Journal of Global Optimization 50, no. 1 (July 11, 2010): 39–57. http://dx.doi.org/10.1007/s10898-010-9579-8.

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21

Georgiev, P. G., and P. M. Pardalos. "Generalized Nash equilibrium problems for lower semi-continuous strategy maps." Journal of Global Optimization 50, no. 1 (March 11, 2011): 119–25. http://dx.doi.org/10.1007/s10898-011-9670-9.

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22

Dreves, Axel, Christian Kanzow, and Oliver Stein. "Nonsmooth optimization reformulations of player convex generalized Nash equilibrium problems." Journal of Global Optimization 53, no. 4 (May 22, 2011): 587–614. http://dx.doi.org/10.1007/s10898-011-9727-9.

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23

Altangerel, L., and G. Battur. "Perturbation approach to generalized Nash equilibrium problems with shared constraints." Optimization Letters 6, no. 7 (June 27, 2012): 1379–91. http://dx.doi.org/10.1007/s11590-012-0510-8.

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24

Aussel, D., R. Correa, and M. Marechal. "Gap Functions for Quasivariational Inequalities and Generalized Nash Equilibrium Problems." Journal of Optimization Theory and Applications 151, no. 3 (September 9, 2011): 474–88. http://dx.doi.org/10.1007/s10957-011-9898-z.

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25

Dreves, Axel. "How to Select a Solution in Generalized Nash Equilibrium Problems." Journal of Optimization Theory and Applications 178, no. 3 (June 12, 2018): 973–97. http://dx.doi.org/10.1007/s10957-018-1327-0.

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26

Börgens, Eike, and Christian Kanzow. "ADMM-Type Methods for Generalized Nash Equilibrium Problems in Hilbert Spaces." SIAM Journal on Optimization 31, no. 1 (January 2021): 377–403. http://dx.doi.org/10.1137/19m1284336.

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27

Martyr, Randall, and John Moriarty. "Nonzero-Sum Games of Optimal Stopping and Generalized Nash Equilibrium Problems." SIAM Journal on Control and Optimization 59, no. 2 (January 2021): 1443–65. http://dx.doi.org/10.1137/18m119803x.

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28

Kanzow, Christian, and Daniel Steck. "Augmented Lagrangian Methods for the Solution of Generalized Nash Equilibrium Problems." SIAM Journal on Optimization 26, no. 4 (January 2016): 2034–58. http://dx.doi.org/10.1137/16m1068256.

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29

Ye, Minglu. "A half-space projection method for solving generalized Nash equilibrium problems." Optimization 66, no. 7 (May 22, 2017): 1119–34. http://dx.doi.org/10.1080/02331934.2017.1326045.

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30

von Heusinger, A., and C. Kanzow. "Relaxation Methods for Generalized Nash Equilibrium Problems with Inexact Line Search." Journal of Optimization Theory and Applications 143, no. 1 (April 22, 2009): 159–83. http://dx.doi.org/10.1007/s10957-009-9553-0.

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31

Guo, Lei. "Mathematical programs with multiobjective generalized Nash equilibrium problems in the constraints." Operations Research Letters 49, no. 1 (January 2021): 11–16. http://dx.doi.org/10.1016/j.orl.2020.11.001.

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32

Han, Deren, Hongchao Zhang, Gang Qian, and Lingling Xu. "An improved two-step method for solving generalized Nash equilibrium problems." European Journal of Operational Research 216, no. 3 (February 2012): 613–23. http://dx.doi.org/10.1016/j.ejor.2011.08.008.

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33

Dreves, Axel. "A best-response approach for equilibrium selection in two-player generalized Nash equilibrium problems." Optimization 68, no. 12 (July 31, 2019): 2269–95. http://dx.doi.org/10.1080/02331934.2019.1646743.

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34

Li, Xingchang. "Existence of Generalized Nash Equilibrium in n-Person Noncooperative Games under Incomplete Preference." Journal of Function Spaces 2018 (October 9, 2018): 1–5. http://dx.doi.org/10.1155/2018/3737253.

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To prove the existence of Nash equilibrium by traditional ways, a common condition that the preference of players must be complete has to be considered. This paper presents a new method to improve it. Based on the incomplete preference corresponding to equivalence class set being a partial order set, we translate the incomplete preference problems into the partial order problems. Using the famous Zorn lemma, we get the existence theorems of fixed point for noncontinuous operators in incomplete preference sets. These new fixed point theorems provide a new way to break through the limitation. Finally, the existence of generalized Nash equilibrium is strictly proved in the n-person noncooperative games under incomplete preference.

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35

Huang, Young-Ye, and Chung-Chien Hong. "A Unified Iterative Treatment for Solutions of Problems of Split Feasibility and Equilibrium in Hilbert Spaces." Abstract and Applied Analysis 2013 (2013): 1–13. http://dx.doi.org/10.1155/2013/613928.

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We at first raise the so called split feasibility fixed point problem which covers the problems of split feasibility, convex feasibility, and equilibrium as special cases and then give two types of algorithms for finding solutions of this problem and establish the corresponding strong convergence theorems for the sequences generated by our algorithms. As a consequence, we apply them to study the split feasibility problem, the zero point problem of maximal monotone operators, and the equilibrium problem and to show that the unique minimum norm solutions of these problems can be obtained through our algorithms. Since the variational inequalities, convex differentiable optimization, and Nash equilibria in noncooperative games can be formulated as equilibrium problems, each type of our algorithms can be considered as a generalized methodology for solving the aforementioned problems.

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36

Dreves, Axel, Francisco Facchinei, Christian Kanzow, and Simone Sagratella. "On the solution of the KKT conditions of generalized Nash equilibrium problems." SIAM Journal on Optimization 21, no. 3 (July 2011): 1082–108. http://dx.doi.org/10.1137/100817000.

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37

WEI, YingYing, LingLing XU, and DeRen HAN. "A decomposition method based on penalization for solving generalized Nash equilibrium problems." SCIENTIA SINICA Mathematica 44, no. 3 (February 1, 2014): 295–305. http://dx.doi.org/10.1360/012012-563.

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38

Kanzow, C., V. Karl, D. Steck, and D. Wachsmuth. "The Multiplier-Penalty Method for Generalized Nash Equilibrium Problems in Banach Spaces." SIAM Journal on Optimization 29, no. 1 (January 2019): 767–93. http://dx.doi.org/10.1137/17m114114x.

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39

Dreves, Axel, and Matthias Gerdts. "A generalized Nash equilibrium approach for optimal control problems of autonomous cars." Optimal Control Applications and Methods 39, no. 1 (July 20, 2017): 326–42. http://dx.doi.org/10.1002/oca.2348.

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40

Nabetani, Koichi, Paul Tseng, and Masao Fukushima. "Parametrized variational inequality approaches to generalized Nash equilibrium problems with shared constraints." Computational Optimization and Applications 48, no. 3 (May 19, 2009): 423–52. http://dx.doi.org/10.1007/s10589-009-9256-3.

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41

Izmailov, Alexey F., and Mikhail V. Solodov. "On error bounds and Newton-type methods for generalized Nash equilibrium problems." Computational Optimization and Applications 59, no. 1-2 (September 10, 2013): 201–18. http://dx.doi.org/10.1007/s10589-013-9595-y.

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42

Dreves, Axel. "Improved error bound and a hybrid method for generalized Nash equilibrium problems." Computational Optimization and Applications 65, no. 2 (September 12, 2014): 431–48. http://dx.doi.org/10.1007/s10589-014-9699-z.

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43

Li, Xun, Jingtao Shi, and Jiongmin Yong. "Mean-field linear-quadratic stochastic differential games in an infinite horizon." ESAIM: Control, Optimisation and Calculus of Variations 27 (2021): 81. http://dx.doi.org/10.1051/cocv/2021078.

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This paper is concerned with two-person mean-field linear-quadratic non-zero sum stochastic differential games in an infinite horizon. Both open-loop and closed-loop Nash equilibria are introduced. The existence of an open-loop Nash equilibrium is characterized by the solvability of a system of mean-field forward-backward stochastic differential equations in an infinite horizon and the convexity of the cost functionals, and the closed-loop representation of an open-loop Nash equilibrium is given through the solution to a system of two coupled non-symmetric algebraic Riccati equations. The existence of a closed-loop Nash equilibrium is characterized by the solvability of a system of two coupled symmetric algebraic Riccati equations. Two-person mean-field linear-quadratic zero-sum stochastic differential games in an infinite horizon are also considered. Both the existence of open-loop and closed-loop saddle points are characterized by the solvability of a system of two coupled generalized algebraic Riccati equations with static stabilizing solutions. Mean-field linear-quadratic stochastic optimal control problems in an infinite horizon are discussed as well, for which it is proved that the open-loop solvability and closed-loop solvability are equivalent.

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44

Lu, Haishu, Kai Zhang, and Rong Li. "Collectively fixed point theorems in noncompact abstract convex spaces with applications." AIMS Mathematics 6, no. 11 (2021): 12422–59. http://dx.doi.org/10.3934/math.2021718.

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<abstract><p>In this paper, by using the KKM theory and the properties of $ \Gamma $-convexity and $ {\frak{RC}} $-mapping, we investigate the existence of collectively fixed points for a family with a finite number of set-valued mappings on the product space of noncompact abstract convex spaces. Consequently, as applications, some existence theorems of generalized weighted Nash equilibria and generalized Pareto Nash equilibria for constrained multiobjective games, some nonempty intersection theorems with applications to the Fan analytic alternative formulation and the existence of Nash equilibria, and some existence theorems of solutions for generalized weak implicit inclusion problems in noncompact abstract convex spaces are given. The results obtained in this paper extend and generalize many corresponding results of the existing literature.</p></abstract>

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45

Sagratella, Simone. "On generalized Nash equilibrium problems with linear coupling constraints and mixed-integer variables." Optimization 68, no. 1 (November 19, 2018): 197–226. http://dx.doi.org/10.1080/02331934.2018.1545125.

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46

Chen, Yi Zeng, and Mei Ju Luo. "Smoothing and sample average approximation methods for solving stochastic generalized Nash equilibrium problems." Journal of Industrial and Management Optimization 12, no. 1 (April 2015): 1–15. http://dx.doi.org/10.3934/jimo.2016.12.1.

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47

Li, Pei-Yu. "Sample average approximation method for a class of stochastic generalized Nash equilibrium problems." Journal of Computational and Applied Mathematics 261 (May 2014): 387–93. http://dx.doi.org/10.1016/j.cam.2013.11.014.

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48

Facchinei, Francisco, and Simone Sagratella. "On the computation of all solutions of jointly convex generalized Nash equilibrium problems." Optimization Letters 5, no. 3 (July 16, 2010): 531–47. http://dx.doi.org/10.1007/s11590-010-0218-6.

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49

Dreves, Axel, and Christian Kanzow. "Nonsmooth optimization reformulations characterizing all solutions of jointly convex generalized Nash equilibrium problems." Computational Optimization and Applications 50, no. 1 (January 5, 2010): 23–48. http://dx.doi.org/10.1007/s10589-009-9314-x.

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50

Krawczyk, Jacek B., and Mabel Tidball. "Economic Problems with Constraints: How Efficiency Relates to Equilibrium." International Game Theory Review 18, no. 04 (October 26, 2016): 1650011. http://dx.doi.org/10.1142/s0219198916500110.

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We consider situations, in which socially important goods (like transportation capacity or hospital beds) are supplied by independent economic agents. There is also a regulator that believes that constraining the goods delivery is desirable. The regulator can compute a constrained Pareto-efficient solution to establish optimal output levels for each agent. We suggest that a coupled-constraint equilibrium (also called a “generalized” Nash or “normalized” equilibrium à la Rosen) may be more relevant for market economies than a Pareto-efficient solution. We examine under which conditions the latter can equal the former. We illustrate our findings using a coordination problem, in which the agents’ outputs depend on externalities. It becomes evident that the correspondence between an efficient and equilibrium solutions cannot be complete if the agents’ activities generate both negative and positive externalities at the same time.

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