The Cone Condition and Nonsmoothness in Linear Generalized Nash Games

Stein, Oliver; Sudermann‐Merx, Nathan

doi:10.1007/s10957-015-0779-8

Cited by 11 publications

(2 citation statements)

References 26 publications

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“…We provide some examples of monotone GNEPs to give a sense of their expressivity. Two of these examples are linear GNEPs [Stein and Sudermann-Merx, 2016, Dreves and Sudermann-Merx, 2016, Dreves, 2017, Stein and Sudermann-Merx, 2018 and the others are nonlinear GNEPs.…”

Section: The Function θmentioning

confidence: 99%

First-Order Algorithms for Nonlinear Generalized Nash Equilibrium Problems

Jordan¹,

Lin²,

Zampetakis³

2022

Preprint

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We consider the problem of computing an equilibrium in a class of nonlinear generalized Nash equilibrium problems (NGNEPs) in which the strategy sets for each player are defined by equality and inequality constraints that may depend on the choices of rival players. While the asymptotic global convergence and local convergence rate of solution procedures have been studied in this setting, the analysis of iteration complexity is still in its infancy. Our contribution is to provide two simple firstorder algorithmic frameworks based on the quadratic penalty method and the augmented Lagrangian method, respectively, with an accelerated mirror-prox algorithm as the inner loop. We provide nonasymptotic theoretical guarantees for these algorithms. More specifically, we establish the global convergence rate of our algorithms for solving (strongly) monotone NGNEPs and we provide iteration complexity bounds expressed in terms of the number of gradient evaluations. Experimental results demonstrate the efficiency of our algorithms.

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Section: The Function θmentioning

confidence: 99%

First-Order Algorithms for Nonlinear Generalized Nash Equilibrium Problems

Jordan¹,

Lin²,

Zampetakis³

2022

Preprint

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“…Linear GNEPs in a completely continuous setting have been widely studied in [8,9,15,35]. In our mixed-integer framework, the problem solved by any player ν is the following min…”

Section: Jointly Convex Linear Gneps With Mixed-integer Variablesmentioning

confidence: 99%

Algorithms for generalized potential games with mixed-integer variables

Sagratella

2017

Comput Optim Appl

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We consider generalized potential games, that constitute a fundamental subclass of generalized Nash equilibrium problems. We propose different methods to compute solutions of generalized potential games with mixedinteger variables, i.e., games in which some variable are continuous while the others are discrete. We investigate which types of equilibria of the game can be computed by minimizing a potential function over the common feasible set. In particular, for a wide class of generalized potential games, we characterize those equilibria that can be computed by minimizing potential functions as Pareto solutions of a particular multi-objective problem, and we show how different potential functions can be used to select equilibria. We propose a new Gauss-Southwell algorithm to compute approximate equilibria of any generalized potential game with mixed-integer variables. We show that this method converges in a finite number of steps and we also give an upper bound on this number of steps. Moreover, we make a thorough analysis on the behaviour of approximate equilibria with respect to exact ones. Finally, we make many numerical experiments to show the viability of the proposed approaches. Keywords Generalized Nash equilibrium problem • Generalized potential game • Mixed-integer nonlinear problem • Parametric optimization The work of the author has been partially supported by Avvio alla Ricerca 2015 Sapienza University of Rome, under grant 488.

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Revisiting Path-Following to Solve the Generalized Nash Equilibrium Problem

Migot

Cojocaru

2021

Springer Proceedings in Mathematics &Amp; Statistics

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The Cone Condition and Nonsmoothness in Linear Generalized Nash Games

Cited by 11 publications

References 26 publications

First-Order Algorithms for Nonlinear Generalized Nash Equilibrium Problems

First-Order Algorithms for Nonlinear Generalized Nash Equilibrium Problems

Algorithms for generalized potential games with mixed-integer variables

Revisiting Path-Following to Solve the Generalized Nash Equilibrium Problem

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