Reducing the complexity of equilibrium problems and applications to best approximation problems
Optimization and Control
2024-01-02 v1
Abstract
We consider scalar equilibrium problems governed by a bifunction in a finite-dimensional framework. By using classical arguments in Convex Analysis, we show that under suitable generalized convexity assumptions imposed on the bifunction, the solutions of the equilibrium problem can be characterized by means of extreme or exposed points of the feasible domain. Our results are relevant for different particular instances, such as variational inequalities and optimization problems, especially for best approximation problems.
Cite
@article{arxiv.2210.10831,
title = {Reducing the complexity of equilibrium problems and applications to best approximation problems},
author = {Valerian-Alin Fodor and Nicolae Popovici},
journal= {arXiv preprint arXiv:2210.10831},
year = {2024}
}