Continuous and discrete systems for quasi variational inequalities with application to game theory
Abstract
A new class of projected dynamical systems of third order is investigated for quasi (parametric) variational inequalities in which the convex set in the classical variational inequality also depends upon the solution explicitly or implicitly. We study the stability of a continuous method of a gradient type. Some iterative implicit and explicit schemes are suggested as counterparts of the continuous case by inertial proximal methods. The convergence analysis of these proposed methods is established under sufficient mild conditions. Moreover, some applications dealing with the generalized Nash equilibrium problems are presented.
Copyright © 2025 Oday Hazaimah. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Cite this article
O. Hazaimah, Continuous and discrete systems for quasi variational inequalities with application to game theory, J. Math. Comput. Sci. 15 (2025), 2. https://doi.org/10.28919/jmcs/8923
BibTeX
@article{Hazaimah2025,
author = {Hazaimah, Oday},
title = {Continuous and discrete systems for quasi variational inequalities with application to game theory},
journal = {J. Math. Comput. Sci.},
volume = {15},
year = {2025},
pages = {2},
doi = {10.28919/jmcs/8923}
}