Variational convergence of bivariate functions: lopsided convergence

摘要

We explore convergence notions for bivariate functions that yield convergence and stability results for their maxinf (or minsup) points. This lays the foundations for the study of the stability of solutions to variational inequalities, the solutions of inclusions, of Nash equilibrium points of non-cooperative games and Walras economic equilibrium points, of fixed points, of solutions to inclusions, the primal and dual solutions of convex optimization problems and of zero-sum games. These applications will be dealt with in a couple of accompanying papers. Keywords Lopsided convergence - Maxinf-points - Ky Fan functions - Variational inequalities - Epi-convergence Mathematics Subject Classification (2000) 65K10 - 90C31 - 91A10 - 47J20 - 47J30 - 49J45 Dedicated to A. Auslender in recognition of his valuable contributions to Mathematical Programming: foundations and numerical procedures.