#### Document Type

Technical Report

#### Abstract

This paper concerns developing two hybrid proximal point methods (PPMs) for finding a common solution of some optimization-related problems. First we construct an algorithm to solve simultaneously an equilibrium problem and a variational inequality problem, combing the extragradient method for variational inequalities with an approximate PPM for equilibrium problems. Next we develop another algorithm based on an alternate approximate PPM for finding a common solution of two different equilibrium problems. We prove the global convergence of both algorithms under pseudomonotonicity assumptions.

#### Number in Series

2009.11

#### Disciplines

Applied Mathematics | Mathematics

#### Recommended Citation

Mordukhovich, Boris S.; Panicucci, Barbara; Passacantando, Mauro; and Pappalardo, Massimo, "Hybrid Proximal Methods for Equilibrium Problems" (2009). *Mathematics Research Reports*. 70.

http://digitalcommons.wayne.edu/math_reports/70

## Comments

This work was supported by the Italian National Research Program PRIN 20079PLLN7 "Nonlinear Optimization, Variational Inequalities, and Equilibrium Problems." The research of the first author was also partially supported by US National Science Foundation under grant DMS-0603846.