Equilibrium Problems, Quasi-Variational Inequalities and Epi-Convergence

Sjur Didrik Flam
Economics Department, Bergen University, Norway

Abstract

We compute equilibrium solutions in problems where such points must be optimal for a given objective and fixed under some specified correspondence. Important examples include so-called quasi-variational inequalities. Under assumptions about quasi-monotonicity of equilibria we show that such outcomes can be located applying only convex minimization iteratively. Each stage of computation invokes two proximal steps, using Bregman functions, one step to predict the next point, the other to correct the prediction. We accommodate numerical errors and approximate data.