An Inertial Projection-Like Method for Solving a Generalized Nash Equilibrium Problem

Authors

  • Premyuda Dechboon Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi, Bangkok 10140, Thailand, KMUTTFixed Point Research Laboratory, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi, Bangkok 10140, Thailand
  • Poom Kumam Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi, Bangkok 10140, Thailand, KMUTTFixed Point Research Laboratory, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi, Bangkok 10140, Thailand, Center of Excellence in Theoretical and Computational Science, Science Laboratory Building, King Mongkut’s University of Technology Thonburi, Bangkok 10140, Thailand
  • Parin Chaipunya Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi, Bangkok 10140, Thailand, Center of Excellence in Theoretical and Computational Science, Science Laboratory Building, King Mongkut’s University of Technology Thonburi, Bangkok 10140, Thailand

Keywords:

Convergence, Inertial method, Nash equilibrium problem, Projection-like method, Quasi-variational inequality

Abstract

In this paper, we propose an algorithm for solving the generalized Nash equilibrium for noncooperative games by means of the quasi variational inequality. Incorporating the inertial steps to a projection-like method, we show the convergence of the generated sequence to the solution of a quasi-variational inequality, and hence the Nash equilibrium. We also implement the algorithm to some test problems, where the numerical experiment portrays that the convergence of our proposed algorithm is about twice as fast compared to the known projection-like method without the inertial steps.

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Published

2022-09-28

How to Cite

Premyuda Dechboon, Poom Kumam, & Parin Chaipunya. (2022). An Inertial Projection-Like Method for Solving a Generalized Nash Equilibrium Problem. Science & Technology Asia, 27(3), 109–120. Retrieved from https://ph02.tci-thaijo.org/index.php/SciTechAsia/article/view/247444

Issue

Section

Physical sciences