Optimization reformulations of the generalized Nash equilibrium problem using Nikaido-Isoda-type functions

DOI10.1007/s10589-007-9145-6zbMath1170.90495OpenAlexW1965826098MaRDI QIDQ839683

Anna von Heusinger, Christian Kanzow

Publication date: 2 September 2009

Published in: Computational Optimization and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10589-007-9145-6

zbMATH Keywords

generalized Nash equilibriajoint constraintsconstrained optimization reformulationnormalized Nash equilibriaregularized Nikaido-Isoda-functionunconstrained optimization reformulation

Mathematics Subject Classification ID

Noncooperative games (91A10) Nonlinear programming (90C30)

Related Items

A penalty method for generalized Nash equilibrium problems, A Newton-type method for quasi-equilibrium problems and applications, An adaptive trust-region method without function evaluations, Jointly convex generalized Nash equilibria and elliptic multiobjective optimal control, On solving generalized Nash equilibrium problems via optimization, Methods for solving generalized Nash equilibrium, The cone condition and nonsmoothness in linear generalized Nash games, A globalized Newton method for the computation of normalized Nash equilibria, A new class of hybrid extragradient algorithms for solving quasi-equilibrium problems, Smoothness properties of a regularized gap function for quasi-variational inequalities, A generalized Nash equilibrium approach for optimal control problems of autonomous cars, A variational inequality method for computing a normalized equilibrium in the generalized Nash game, Supply chain network capacity competition with outsourcing: a variational equilibrium framework, Exact Penalization of Generalized Nash Equilibrium Problems, Interior point methods for equilibrium problems, Gap functions and penalization for solving equilibrium problems with nonlinear constraints, A trust-region LP-Newton method for constrained nonsmooth equations under Hölder metric subregularity, An algorithm for equilibrium selection in generalized Nash equilibrium problems, Minimax Problems with Coupled Linear Constraints: Computational Complexity and Duality, Rational Generalized Nash Equilibrium Problems, Equilibrium modeling and solution approaches inspired by nonconvex bilevel programming, On the polyhedral homotopy method for solving generalized Nash equilibrium problems of polynomials, An improved two-step method for solving generalized Nash equilibrium problems, Newton's method for computing a normalized equilibrium in the generalized Nash game through fixed point formulation, Unicidad para problemas de cuasi-equilibrio, Convex generalized Nash equilibrium problems and polynomial optimization, Optimization reformulations of the generalized Nash equilibrium problem using regularized indicator Nikaidô-Isoda function, A barrier function method for generalized Nash equilibrium problems, Nonsmooth optimization reformulations characterizing all solutions of jointly convex generalized Nash equilibrium problems, Gap functions for quasivariational inequalities and generalized Nash equilibrium problems, Primal-dual proximal splitting and generalized conjugation in non-smooth non-convex optimization, On a smooth dual gap function for a class of player convex generalized Nash equilibrium problems, Optimality Conditions and Constraint Qualifications for Generalized Nash Equilibrium Problems and Their Practical Implications, Generalized Nash equilibrium problems, The noncooperative transportation problem and linear generalized Nash games, A competitive multiperiod supply chain network model with freight carriers and green technology investment option, Gap functions for quasi-equilibria, On the computation of all solutions of jointly convex generalized Nash equilibrium problems, Restricted generalized Nash equilibria and controlled penalty algorithm, Perturbation approach to generalized Nash equilibrium problems with shared constraints, Gap function approach to the generalized Nash equilibrium problem, Nonsmooth optimization reformulations of player convex generalized Nash equilibrium problems, Parametrized variational inequality approaches to generalized Nash equilibrium problems with shared constraints, A smoothing method for a class of generalized Nash equilibrium problems, Generalized Nash equilibrium problems, Some projection-like methods for the generalized Nash equilibria, The Gauss-Seidel method for generalized Nash equilibrium problems of polynomials, A Game of International Climate Policy Solved by a Homogeneous Oracle-Based Method for Variational Inequalities, Economics of collective monitoring: a study of environmentally constrained electricity generators, A projected dynamic system associated with a cybersecurity investment model with budget constraints and fixed demands, A Globally Convergent LP-Newton Method, Augmented Lagrangian Methods for the Solution of Generalized Nash Equilibrium Problems, On differentiability properties of player convex generalized Nash equilibrium problems, Solving linear generalized Nash equilibrium problems numerically, Relaxation methods for generalized Nash equilibrium problems with inexact line search, Supply chain network competition among blood service organizations: a generalized Nash equilibrium framework, Evolutionary Algorithm for Generalized Nash Equilibrium Problems, Interactions Between Bilevel Optimization and Nash Games, Addressing supply-side risk in uncertain power markets: stochastic Nash models, scalable algorithms and error analysis, Interior proximal methods for equilibrium programming: part I

Cites Work

• Unnamed Item
• Generalized Nash equilibrium problems and Newton methods
• Approximations of Nash equilibria
• Distributed algorithms for the computation of noncooperative equilibria
• Relaxation techniques and asynchronous algorithms for on-line computation of non-cooperative equilibria
• Generalized Nash games and quasi-variational inequalities
• Equivalent differentiable optimization problems and descent methods for asymmetric variational inequality problems
• Theoretical and numerical investigation of the D-gap function for box constrained variational inequalities
• Unconstrained optimization reformulations of variational inequality problems
• Equivalence of variational inequality problems to unconstrained minimization
• Equilibrium programming using proximal-like algorithms
• Gap functions for equilibrium problems
• Nonmonotone globalization techniques for the Barzilai-Borwein gradient method
• A nonsmooth version of Newton's method
• Quasi-variational inequalities, generalized Nash equilibria, and multi-leader-follower games
• A robust optimization approach to dynamic pricing and inventory control with no backorders
• Note on noncooperative convex games
• On generalized Nash games and variational inequalities
• R-linear convergence of the Barzilai and Borwein gradient method
• Dynamic Pricing and Inventory Control: Uncertainty and Competition
• The Barzilai and Borwein Gradient Method for the Large Scale Unconstrained Minimization Problem
• Nonsmooth Equations: Motivation and Algorithms
• Two-Point Step Size Gradient Methods
• On relaxation algorithms in computation of noncooperative equilibria
• Convergence Analysis of Some Algorithms for Solving Nonsmooth Equations
• Finite-Dimensional Variational Inequalities and Complementarity Problems
• On the Barzilai and Borwein choice of steplength for the gradient method
• Existence and Uniqueness of Equilibrium Points for Concave N-Person Games
• Point-to-Set Maps in Mathematical Programming