Solving non-monotone equilibrium problems via a DIRECT-type approach
Abstract
A global optimization approach for solving non-monotone equilibrium problems (EPs) is proposed. The class of (regularized) gap functions is used to reformulate any EP as a constrained global optimization program and some bounds on the Lipschitz constant of such functions are provided. The proposed global optimization approach is a combination of an improved version of the \texttt{DIRECT} algorithm, which exploits local bounds of the Lipschitz constant of the objective function, with local minimizations. Unlike most existing solution methods for EPs, no monotonicity-type condition is assumed in this paper. Preliminary numerical results on several classes of EPs show the effectiveness of the approach.
Cite
@article{arxiv.2002.12198,
title = {Solving non-monotone equilibrium problems via a DIRECT-type approach},
author = {Stefano Lucidi and Mauro Passacantando and Francesco Rinaldi},
journal= {arXiv preprint arXiv:2002.12198},
year = {2020}
}
Comments
Technical Report of Department of Computer Science, University of Pisa, Italy