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Journal articles on the topic 'Generalized Nash equilibrium problems'

Author: Grafiati

Published: 10 March 2023

Last updated: 31 July 2025

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1

Facchinei, Francisco, and Christian Kanzow. "Generalized Nash Equilibrium Problems." Annals of Operations Research 175, no. 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 (2007): 173–210. http://dx.doi.org/10.1007/s10288-007-0054-4.

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3

Nie, Jiawang, Xindong Tang, and Suhan Zhong. "Rational Generalized Nash Equilibrium Problems." SIAM Journal on Optimization 33, no. 3 (2023): 1587–620. http://dx.doi.org/10.1137/21m1456285.

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4

Pan, Chengqing, and Haishu Lu. "On the existence of solutions for systems of generalized vector quasi-variational equilibrium problems in abstract convex spaces with applications." AIMS Mathematics 9, no. 11 (2024): 29942–73. http://dx.doi.org/10.3934/math.20241447.

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<p>In this paper, we first introduced systems of generalized vector quasi-variational equilibrium problems as well as systems of vector quasi-variational equilibrium problems as their special cases in abstract convex spaces. Next, we established some existence theorems of solutions for systems of generalized vector quasi-variational equilibrium problems and systems of vector quasi-variational equilibrium problems in non-compact abstract convex spaces. Furthermore, we applied the obtained existence theorem of solutions for systems of vector quasi-variational equilibrium problems to solve

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5

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

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6

Singh, Shipra, Aviv Gibali, and Simeon Reich. "Multi-Time Generalized Nash Equilibria with Dynamic Flow Applications." Mathematics 9, no. 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 r

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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

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

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9

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

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10

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

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11

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

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12

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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13

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 (2017): 3893–908. http://dx.doi.org/10.1109/tsp.2017.2695451.

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14

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

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15

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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16

Couellan, Nicolas. "A note on supervised classification and Nash-equilibrium problems." RAIRO - Operations Research 51, no. 2 (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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17

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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18

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

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19

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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20

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

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21

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

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22

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

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23

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

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24

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

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25

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

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26

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 (2011): 474–88. http://dx.doi.org/10.1007/s10957-011-9898-z.

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27

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

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28

Lisboa, Adriano C., Fellipe F. G. Santos, Douglas A. G. Vieira, Rodney R. Saldanha, and Felipe A. C. Pereira. "An Enhanced Gradient Algorithm for Computing Generalized Nash Equilibrium Applied to Electricity Market Games." Energies 18, no. 3 (2025): 727. https://doi.org/10.3390/en18030727.

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This paper introduces an enhanced algorithm for computing generalized Nash equilibria for multiple player nonlinear games, which degenerates in a gradient algorithm for single player games (i.e., optimization problems) or potential games (i.e., equivalent to minimizing the respective potential function), based on the Rosen gradient algorithm. Analytical examples show that it has similar theoretical guarantees of finding a generalized Nash equilibrium when compared to the relaxation algorithm, while numerical examples show that it is faster. Furthermore, the proposed algorithm is as fast as, bu

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29

CHAIPUNYA, PARIN, NANTAPORN CHUENSUPANTHARAT, and PRINTAPORN SANGUANSUTTIGUL. "Graphical Ekeland's variational principle with a generalized $w$-distance and a new approach to quasi-equilibrium problems." Carpathian Journal of Mathematics 39, no. 1 (2022): 95–107. http://dx.doi.org/10.37193/cjm.2023.01.06.

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In this paper, we introduce the generalized Ekeland's variational principle in several forms. The general setting of our results includes a graphical metric structure and also employs a generalized $w$-distance. We then applied the proposed variational principles to obtain existence theorems for a class of quasi-equilibrium problems whose constraint maps are induced from the graphical structure. The conditions used in our existence results are based on a very general concept called a convergence class. Finally, we deduce the existence of a generalized Nash equilibrium via its quasi-equilibrium

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30

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. Fi

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31

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

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32

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

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33

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 (2021): 1443–65. http://dx.doi.org/10.1137/18m119803x.

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34

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

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35

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

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36

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 (2009): 159–83. http://dx.doi.org/10.1007/s10957-009-9553-0.

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37

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

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38

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 (2012): 613–23. http://dx.doi.org/10.1016/j.ejor.2011.08.008.

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39

Lampariello, Lorenzo, Simone Sagratella, and Valerio Giuseppe Sasso. "Addressing Hierarchical Jointly Convex Generalized Nash Equilibrium Problems with Nonsmooth Payoffs." SIAM Journal on Optimization 35, no. 1 (2025): 445–75. https://doi.org/10.1137/23m1574026.

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40

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

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41

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 exis

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42

Passacantando, Mauro, and Fabio Raciti. "Lipschitz Continuity Results for a Class of Parametric Variational Inequalities and Applications to Network Games." Algorithms 16, no. 10 (2023): 458. http://dx.doi.org/10.3390/a16100458.

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We consider a class of finite-dimensional variational inequalities where both the operator and the constraint set can depend on a parameter. Under suitable assumptions, we provide new estimates for the Lipschitz constant of the solution, which considerably improve previous ones. We then consider the problem of computing the mean value of the solution with respect to the parameter and, to this end, adapt an algorithm devised to approximate a Lipschitz function whose analytic expression is unknown, but can be evaluated in arbitrarily chosen sample points. Finally, we apply our results to a class

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43

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

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44

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 (2011): 1082–108. http://dx.doi.org/10.1137/100817000.

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45

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 (2014): 295–305. http://dx.doi.org/10.1360/012012-563.

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46

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 (2019): 767–93. http://dx.doi.org/10.1137/17m114114x.

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47

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 (2009): 423–52. http://dx.doi.org/10.1007/s10589-009-9256-3.

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48

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 (2013): 201–18. http://dx.doi.org/10.1007/s10589-013-9595-y.

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49

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

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50

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 (2017): 326–42. http://dx.doi.org/10.1002/oca.2348.

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