Topological stability results about approximate solutions of parametrized minimization problems

Abstract

The useful and classical question of the stability of approximate solutions to a parametrized minimization problem is revisited and examined under various facets. New notions of continuity for functions and multifunctions are involved in this study. Incidentally, a characterization of variational convergence is presented. Some persistence results complete this circular tour.

Keywords:

• Epiconvergence
• limits of sets
• persistence
• perturbed optimization problems
• regularity
• stability
• variational convergence

AMS Subject Classification:

• Primary:49 B 50
• Secondary:90 C 31