A new algorithm to solve the generalized Nash equilibrium problem
type: Item
instance of: scholarly article
title: A new algorithm to solve the generalized Nash equilibrium problem
zbMATH Open document ID: 1459.91079
DOI: 10.1155/2020/1073412
author: Luping Liu
author: Wensheng Jia
published in: Mathematical Problems in Engineering
publication date: 2020-10-14T00:00:00Z
review text: Summary: We try a new algorithm to solve the generalized Nash equilibrium problem (GNEP) in the paper. First, the GNEP is turned into the nonlinear complementarity problem by using the Karush-Kuhn-Tucker (KKT) condition. Then, the nonlinear complementarity problem is converted into the nonlinear equation problem by using the complementarity function method. For the nonlinear equation equilibrium problem, we design a coevolutionary immune quantum particle swarm optimization algorithm (CIQPSO) by involving the immune memory function and the antibody density inhibition mechanism into the quantum particle swarm optimization algorithm. Therefore, this algorithm has not only the properties of the immune particle swarm optimization algorithm, but also improves the abilities of iterative optimization and convergence speed. With the probability density selection and quantum uncertainty principle, the convergence of the CIQPSO algorithm is analyzed. Finally, some numerical experiment results indicate that the CIQPSO algorithm is superior to the immune particle swarm algorithm, the Newton method for normalized equilibrium, or the quasivariational inequalities penalty method. Furthermore, this algorithm also has faster convergence and better off-line performance.
Mathematics Subject Classification ID: 91B50
Mathematics Subject Classification ID: 90C33
zbMATH DE Number: 7260942
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2020/1073412
OpenAlex ID: W3090850387
cites work: A Social Equilibrium Existence Theorem*
cites work: Real and Complex Monotone Communication Games
cites work: A generalized Nash equilibrium approach for optimal control problems of autonomous cars
cites work: Computing equilibria: a computational complexity perspective
cites work: Penalty Methods for the Solution of Generalized Nash Equilibrium Problems
cites work: On the existence of projected solutions of quasi-variational inequalities and generalized Nash equilibrium problems
cites work: A parametrized variational inequality approach to track the solution set of a generalized Nash equilibrium problem
cites work: Optimization reformulations of the generalized Nash equilibrium problem using regularized indicator Nikaidô-Isoda function
cites work: A best-response approach for equilibrium selection in two-player generalized Nash equilibrium problems
cites work: On error bounds and Newton-type methods for generalized Nash equilibrium problems
cites work: Introduction to evolutionary computing
cites work: On Structure and Computation of Generalized Nash Equilibria
cites work: Augmented Lagrangian methods for the solution of generalized Nash equilibrium problems
cites work: Quasi-variational inequalities, generalized Nash equilibria, and multi-leader-follower games
cites work: On the multiplier-penalty-approach for quasi-variational inequalities
cites work: Q2992496
cites work: Generalized Nash equilibrium problems and Newton methods
cites work: Some projection-like methods for the generalized Nash equilibria
description: scientific article; zbMATH DE number 7260942