Mathematical programming, ISSN 1436-4646, 2007, Volume 117, Issue 1-2, pp. 163 - 194

The generalized Nash equilibrium problem, where the feasible sets of the players may depend on the other...

Nonisolated solution | Semismooth Newton method | Mathematical and Computational Physics | Mathematics | Generalized Nash equilibrium | Internet switching | Mathematical Methods in Physics | Levenberg–Marquardt method | 91A10 | 90C30 | Mathematics of Computing | Calculus of Variations and Optimal Control; Optimization | Numerical Analysis | 49M05 | 91A80 | Combinatorics | Levenberg-Marquardt method | EXISTENCE | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | generalized Nash equilibrium | GAMES | nonisolated solution | semismooth Newton method | ALGORITHMS | internet switching | Game theory | Analysis | Methods | Studies | Equilibrium | Mathematical programming

Nonisolated solution | Semismooth Newton method | Mathematical and Computational Physics | Mathematics | Generalized Nash equilibrium | Internet switching | Mathematical Methods in Physics | Levenberg–Marquardt method | 91A10 | 90C30 | Mathematics of Computing | Calculus of Variations and Optimal Control; Optimization | Numerical Analysis | 49M05 | 91A80 | Combinatorics | Levenberg-Marquardt method | EXISTENCE | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | generalized Nash equilibrium | GAMES | nonisolated solution | semismooth Newton method | ALGORITHMS | internet switching | Game theory | Analysis | Methods | Studies | Equilibrium | Mathematical programming

Journal Article

SIAM journal on optimization, ISSN 1095-7189, 2016, Volume 26, Issue 4, pp. 2034 - 2058

We propose an augmented Lagrangian-type algorithm for the solution of generalized Nash equilibrium problems (GNEPs...

Nash equilibrium problem | Global convergence | Generalized nash equilibrium problem | Augmented lagrangian method | Jointly convex problem | MATHEMATICS, APPLIED | NEWTON METHODS | augmented Lagrangian method | generalized Nash equilibrium problem | global convergence | GAMES | jointly convex problem | Mathematics - Optimization and Control

Nash equilibrium problem | Global convergence | Generalized nash equilibrium problem | Augmented lagrangian method | Jointly convex problem | MATHEMATICS, APPLIED | NEWTON METHODS | augmented Lagrangian method | generalized Nash equilibrium problem | global convergence | GAMES | jointly convex problem | Mathematics - Optimization and Control

Journal Article

Journal of Global Optimization, ISSN 0925-5001, 11/2013, Volume 57, Issue 3, pp. 843 - 861

...–Isoda function, and this is demonstrated to guarantee existence of a solution. Using this function, we present two constrained optimization reformulations of the generalized Nash equilibrium problem (GNEP for short...

91A10 | Optimization reformulations | 90C30 | Operations Research/Decision Theory | Regularized indicator Nikaidô–Isoda function | Normalized Nash equilibria | Computer Science, general | Quasi-variational inequality problem | Generalized Nash equilibrium problem | Optimization | Economics / Management Science | Real Functions | Regularized indicator Nikaidô-Isoda function | Studies | Game theory | Mathematical models | Constraints | Minima | Mathematical analysis | Indicators

91A10 | Optimization reformulations | 90C30 | Operations Research/Decision Theory | Regularized indicator Nikaidô–Isoda function | Normalized Nash equilibria | Computer Science, general | Quasi-variational inequality problem | Generalized Nash equilibrium problem | Optimization | Economics / Management Science | Real Functions | Regularized indicator Nikaidô-Isoda function | Studies | Game theory | Mathematical models | Constraints | Minima | Mathematical analysis | Indicators

Journal Article

Journal of Optimization Theory and Applications, ISSN 0022-3239, 9/2018, Volume 178, Issue 3, pp. 973 - 997

We propose a new solution concept for generalized Nash equilibrium problems. This concept leads, under suitable assumptions, to unique solutions...

Tracing procedure | Equilibrium selection problem | 65K05 | Mathematics | Theory of Computation | Generalized Nash equilibrium problem | Optimization | New solution concept | 90C31 | 91A10 | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | 90C33 | Applications of Mathematics | Engineering, general | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | QUASI-VARIATIONAL INEQUALITIES | Game theory | Aerospace engineering | Economic models | Equilibrium | Weight reduction

Tracing procedure | Equilibrium selection problem | 65K05 | Mathematics | Theory of Computation | Generalized Nash equilibrium problem | Optimization | New solution concept | 90C31 | 91A10 | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | 90C33 | Applications of Mathematics | Engineering, general | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | QUASI-VARIATIONAL INEQUALITIES | Game theory | Aerospace engineering | Economic models | Equilibrium | Weight reduction

Journal Article

Optimization Methods and Software, ISSN 1055-6788, 09/2016, Volume 31, Issue 5, pp. 1036 - 1063

This paper considers the numerical solution of linear generalized Nash equilibrium problems (LGNEPs...

penalty method | linear generalized Nash equilibrium problem | projected subgradient method | economic market model | potential reduction algorithm | MATHEMATICS, APPLIED | RELAXATION ALGORITHMS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | 91A10 | 90C51 | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | 91A06 | 90C56 | OPTIMIZATION | Economic models | Game theory | Equilibrium | Economics | Algorithms | Constraint modelling | Markets | Mathematical models | Derivatives | Optimization | Convergence

penalty method | linear generalized Nash equilibrium problem | projected subgradient method | economic market model | potential reduction algorithm | MATHEMATICS, APPLIED | RELAXATION ALGORITHMS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | 91A10 | 90C51 | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | 91A06 | 90C56 | OPTIMIZATION | Economic models | Game theory | Equilibrium | Economics | Algorithms | Constraint modelling | Markets | Mathematical models | Derivatives | Optimization | Convergence

Journal Article

6.
Full Text
A generalized Nash equilibrium approach for optimal control problems of autonomous cars

Optimal control applications & methods, ISSN 0143-2087, 2018, Volume 39, Issue 1, pp. 326 - 342

.... For these problems, we use the generalized Nash equilibrium approach and provide a reformulation of normalized Nash equilibria as solutions to a single optimal control problem...

traffic scenarios | ordinary differential equations | optimal control | autonomous vehicles | generalized Nash equilibrium problem | existence of an equilibrium | MATHEMATICS, APPLIED | DESIGN | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | vehicles,autonomous existence of an equilibrium | STATE | ERROR-BOUNDS | generalized Nash equilibriumproblem | optima control | AUTOMATION & CONTROL SYSTEMS | EULER APPROXIMATION | Driverless cars | Game theory | Economic models | Traffic models | Autonomous cars | Automobiles | Equilibrium | Convergence | Automotive engineering | Vehicles | Optimal control | Differential equations | Ordinary differential equations | Convexity

traffic scenarios | ordinary differential equations | optimal control | autonomous vehicles | generalized Nash equilibrium problem | existence of an equilibrium | MATHEMATICS, APPLIED | DESIGN | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | vehicles,autonomous existence of an equilibrium | STATE | ERROR-BOUNDS | generalized Nash equilibriumproblem | optima control | AUTOMATION & CONTROL SYSTEMS | EULER APPROXIMATION | Driverless cars | Game theory | Economic models | Traffic models | Autonomous cars | Automobiles | Equilibrium | Convergence | Automotive engineering | Vehicles | Optimal control | Differential equations | Ordinary differential equations | Convexity

Journal Article

Computational optimization and applications, ISSN 1573-2894, 2009, Volume 48, Issue 3, pp. 423 - 452

We consider the generalized Nash equilibrium problem (GNEP), in which each player’s strategy set may depend on the rivals...

Lagrange multiplier | Resource-directed parametrizations | Variational inequality | Convex and Discrete Geometry | Operations Research/Decision Theory | Price-directed parametrizations | Karush-Kuhn-Tucker condition | Mathematics | Operations Research, Mathematical Programming | Statistics, general | Generalized Nash equilibrium | Optimization | COMPLEMENTARITY-PROBLEMS | MATHEMATICS, APPLIED | RELAXATION ALGORITHMS | MARKETS | GAMES | SHADOW PRICES | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MODELS | Game theory | Universities and colleges | Equality | Studies | Mathematical analysis | Computation | Inequalities | Strategy | Benchmarking | Mathematical models

Lagrange multiplier | Resource-directed parametrizations | Variational inequality | Convex and Discrete Geometry | Operations Research/Decision Theory | Price-directed parametrizations | Karush-Kuhn-Tucker condition | Mathematics | Operations Research, Mathematical Programming | Statistics, general | Generalized Nash equilibrium | Optimization | COMPLEMENTARITY-PROBLEMS | MATHEMATICS, APPLIED | RELAXATION ALGORITHMS | MARKETS | GAMES | SHADOW PRICES | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MODELS | Game theory | Universities and colleges | Equality | Studies | Mathematical analysis | Computation | Inequalities | Strategy | Benchmarking | Mathematical models

Journal Article

European Journal of Operational Research, ISSN 0377-2217, 04/2018, Volume 266, Issue 2, pp. 543 - 553

....•A high-dimensional set of so-called basic Nash equilibria is computed.•The problem of selecting an appropriate Nash equilibrium is discussed extensively...

Transportation | Noncooperative game theory | Subgradient method | Linear generalized Nash equilibrium problem | Transportation problem with several forwarders | RELAXATION ALGORITHMS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | INFORMATION | SYSTEMS | OPTIMIZATION | EQUILIBRIUM PROBLEMS | SELECTION

Transportation | Noncooperative game theory | Subgradient method | Linear generalized Nash equilibrium problem | Transportation problem with several forwarders | RELAXATION ALGORITHMS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | INFORMATION | SYSTEMS | OPTIMIZATION | EQUILIBRIUM PROBLEMS | SELECTION

Journal Article

Automatica (Oxford), ISSN 0005-1098, 2012, Volume 48, Issue 1, pp. 45 - 55

.... A widely employed solution concept for such generalized Nash games is the generalized Nash equilibrium (GNE...

Refinement of an equilibrium | Shared constraints | Variational equilibrium | Generalized Nash games | COMPLEMENTARITY-PROBLEMS | INEQUALITIES | GAMES | AUTOMATION & CONTROL SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Game theory | Economics | Rest | Lagrange multipliers | Mathematical analysis | Inequalities | Games | Strategy | Players

Refinement of an equilibrium | Shared constraints | Variational equilibrium | Generalized Nash games | COMPLEMENTARITY-PROBLEMS | INEQUALITIES | GAMES | AUTOMATION & CONTROL SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Game theory | Economics | Rest | Lagrange multipliers | Mathematical analysis | Inequalities | Games | Strategy | Players

Journal Article

International journal of energy research, ISSN 0363-907X, 2018, Volume 42, Issue 15, pp. 4584 - 4596

Summary This paper presents a generalized Nash equilibrium problem (GNEP) approach for the management of plug...

distribution network | generalized Nash equilibrium | reformulation | plug‐in electric vehicle charging | plug-in electric vehicle charging | ENERGY & FUELS | NUCLEAR SCIENCE & TECHNOLOGY | SYSTEMS | Electric vehicles | Game theory | Operational costs | Stress concentration | Networks | Economic models | Load distribution | Charging | Electronic devices | Computer simulation | Methodology | Decision making | Tariff | Management | Equilibrium | Optimization | Loads (forces) | Load distribution (forces) | Algorithms | Solutions | Dynamics | Distribution | Pricing | Electric power distribution

distribution network | generalized Nash equilibrium | reformulation | plug‐in electric vehicle charging | plug-in electric vehicle charging | ENERGY & FUELS | NUCLEAR SCIENCE & TECHNOLOGY | SYSTEMS | Electric vehicles | Game theory | Operational costs | Stress concentration | Networks | Economic models | Load distribution | Charging | Electronic devices | Computer simulation | Methodology | Decision making | Tariff | Management | Equilibrium | Optimization | Loads (forces) | Load distribution (forces) | Algorithms | Solutions | Dynamics | Distribution | Pricing | Electric power distribution

Journal Article

Applied soft computing, ISSN 1568-4946, 2016, Volume 39, pp. 21 - 35

... (generalized Nash equilibrium problems).•Proposes a simpler solution to GNEP's based on flexible constrained optimization, avoiding multilevel optimization typical complexity...

Generalized Nash equilibrium problems | Global optimization | GNEP | Adaptive simulated annealing | Nash equilibria | Metaheuristics | RELAXATION ALGORITHMS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Game theory | Case studies | Electrical engineering | Annealing | Management science | Algorithms | Analysis | Mathematical optimization

Generalized Nash equilibrium problems | Global optimization | GNEP | Adaptive simulated annealing | Nash equilibria | Metaheuristics | RELAXATION ALGORITHMS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Game theory | Case studies | Electrical engineering | Annealing | Management science | Algorithms | Analysis | Mathematical optimization

Journal Article

Mathematical Methods of Operations Research, ISSN 1432-2994, 4/2017, Volume 85, Issue 2, pp. 207 - 221

In this paper we consider linear generalized Nash equilibrium problems, i.e., the cost and the constraint functions of all players in a game are assumed to be linear...

Calculus of Variations and Optimal Control; Optimization | Finite termination | Linear generalized Nash equilibrium problem | Mathematics | Operation Research/Decision Theory | Entire solution set | Business and Management, general | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Game theory | Algorithms | Aerospace engineering | Economic models | Games | Markets | Mathematical models | Cost engineering | Marketing | Players

Calculus of Variations and Optimal Control; Optimization | Finite termination | Linear generalized Nash equilibrium problem | Mathematics | Operation Research/Decision Theory | Entire solution set | Business and Management, general | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Game theory | Algorithms | Aerospace engineering | Economic models | Games | Markets | Mathematical models | Cost engineering | Marketing | Players

Journal Article

Journal of Global Optimization, ISSN 0925-5001, 8/2012, Volume 53, Issue 4, pp. 587 - 614

Using a regularized Nikaido-Isoda function, we present a (nonsmooth) constrained optimization reformulation of the player convex generalized Nash equilibrium problem (GNEP...

Constant rank constraint qualification | PC 1 mapping | Operations Research/Decision Theory | Optimization reformulation | Player convex | Jointly convex | Continuity | Computer Science, general | Generalized Nash equilibrium problem | Optimization | Economics / Management Science | Real Functions | PC1mapping | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | PCmapping | Game theory | Studies

Constant rank constraint qualification | PC 1 mapping | Operations Research/Decision Theory | Optimization reformulation | Player convex | Jointly convex | Continuity | Computer Science, general | Generalized Nash equilibrium problem | Optimization | Economics / Management Science | Real Functions | PC1mapping | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | PCmapping | Game theory | Studies

Journal Article

SIAM Journal on Optimization, ISSN 1052-6234, 2015, Volume 25, Issue 3, pp. 1826 - 1856

Building upon the results in [M. Hintermuller and T. Surowiec, Pac. J. Optim., 9 (2013), pp. 251-273], a class of noncooperative Nash equilibrium problems...

Path-following | GNEP | Spot markets | Nonsmooth Newton methods | PDE-constrained optimization | Variational equilibrium | State constraints | Jointly convex | Generalized Nash equilibrium problem | Multiobjective PDE-constrained optimization | MATHEMATICS, APPLIED | variational equilibrium | GAMES | multiobjective PDE-constrained optimization | state constraints | path-following | POINTWISE CONTROL | ELLIPTIC CONTROL-PROBLEMS | jointly convex | nonsmooth Newton methods | MINIMIZATION | generalized Nash equilibrium problem | spot markets | OPTIMIZATION

Path-following | GNEP | Spot markets | Nonsmooth Newton methods | PDE-constrained optimization | Variational equilibrium | State constraints | Jointly convex | Generalized Nash equilibrium problem | Multiobjective PDE-constrained optimization | MATHEMATICS, APPLIED | variational equilibrium | GAMES | multiobjective PDE-constrained optimization | state constraints | path-following | POINTWISE CONTROL | ELLIPTIC CONTROL-PROBLEMS | jointly convex | nonsmooth Newton methods | MINIMIZATION | generalized Nash equilibrium problem | spot markets | OPTIMIZATION

Journal Article

4OR, ISSN 1614-2411, 2007, Volume 5, Issue 3, pp. 173 - 210

The Generalized Nash equilibrium problem is an important model that has its roots in the economic sciences but is being fruitfully used in many different fields...

Nikaido–Isoda-function | Industrial and Production Engineering | Generalized Nash equilibrium problem | Equilibrium | Optimization | Economics / Management Science | 91A10 | 90C30 | Variational inequality | Operations Research/Decision Theory | Jointly convex constraints | Quasi-variational inequality | 91B50 | Nikaido-Isoda-function | EXISTENCE | RELAXATION ALGORITHMS | MARKET | EQUATIONS | variational inequality | MODEL | TIKHONOV WELL-POSEDNESS | jointly convex constraints | VARIATIONAL-INEQUALITIES | SHADOW PRICES | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | quasi-variational inequality | equilibrium | DISCONTINUOUS ECONOMIC GAMES | COURNOT EQUILIBRIA | Equilibrium (Economics) | Analysis | Algorithms | Studies

Nikaido–Isoda-function | Industrial and Production Engineering | Generalized Nash equilibrium problem | Equilibrium | Optimization | Economics / Management Science | 91A10 | 90C30 | Variational inequality | Operations Research/Decision Theory | Jointly convex constraints | Quasi-variational inequality | 91B50 | Nikaido-Isoda-function | EXISTENCE | RELAXATION ALGORITHMS | MARKET | EQUATIONS | variational inequality | MODEL | TIKHONOV WELL-POSEDNESS | jointly convex constraints | VARIATIONAL-INEQUALITIES | SHADOW PRICES | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | quasi-variational inequality | equilibrium | DISCONTINUOUS ECONOMIC GAMES | COURNOT EQUILIBRIA | Equilibrium (Economics) | Analysis | Algorithms | Studies

Journal Article

Journal of Optimization Theory and Applications, ISSN 0022-3239, 3/2010, Volume 144, Issue 3, pp. 511 - 531

We consider an optimization reformulation approach for the generalized Nash equilibrium problem (GNEP...

Generalized Nash equilibrium problems | Regularized gap functions | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Mathematics | Theory of Computation | Engineering, general | Applications of Mathematics | Quasivariational inequalities | Optimization | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | VARIATIONAL INEQUALITY | ALGORITHMS | Game theory | Algorithms | Studies | Equilibrium

Generalized Nash equilibrium problems | Regularized gap functions | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Mathematics | Theory of Computation | Engineering, general | Applications of Mathematics | Quasivariational inequalities | Optimization | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | VARIATIONAL INEQUALITY | ALGORITHMS | Game theory | Algorithms | Studies | Equilibrium

Journal Article

Computational Optimization and Applications, ISSN 0926-6003, 4/2018, Volume 69, Issue 3, pp. 629 - 652

The generalized Nash equilibrium problem (GNEP) is often difficult to solve by Newton-type methods since the problem tends to have locally nonunique solutions...

Global convergence | Nonmonotone strategy | Operations Research/Decision Theory | Convex and Discrete Geometry | Local superlinear convergence | Trust-region algorithm | Mathematics | Operations Research, Management Science | Statistics, general | Generalized Nash equilibrium problem | Optimization | Quasi-variational inequalities | CONSTRAINED NONLINEAR EQUATIONS | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | LEVENBERG-MARQUARDT METHOD | CONVEX CONSTRAINTS | Algorithms | Game theory | Analysis | Methods | Economic models | Properties (attributes) | Nonlinear programming | Convergence

Global convergence | Nonmonotone strategy | Operations Research/Decision Theory | Convex and Discrete Geometry | Local superlinear convergence | Trust-region algorithm | Mathematics | Operations Research, Management Science | Statistics, general | Generalized Nash equilibrium problem | Optimization | Quasi-variational inequalities | CONSTRAINED NONLINEAR EQUATIONS | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | LEVENBERG-MARQUARDT METHOD | CONVEX CONSTRAINTS | Algorithms | Game theory | Analysis | Methods | Economic models | Properties (attributes) | Nonlinear programming | Convergence

Journal Article