On a Class of Random Variational Inequalities on Random Sets

Abstract

We study a class of random variational inequalities on random sets and give measurability, existence, and uniqueness results in a Hilbert space setting. In the special case where the random and the deterministic variables are separated, we present a discretization technique based on averaging and truncation, prove a Mosco convergence result for the feasible random set, and establish norm convergence of the approximation procedure.

Keywords:

• Averaging
• Coerciveness
• Measurability
• Mosco convergence
• Random set
• Random variational inequality
• Truncation

AMS Subject Classification:

• 49J40
• 49J55
• 49M25
• 60H25

ACKNOWLEDGMENTS

This paper has been written while one of the authors, F.R., was on leave at the University of the Federal Armed Forces in Munich, Germany, supported by the University of Catania (Contributo per l'aggiornamento all'estero dei docenti) and by GNAMPA (Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le sue Applicazioni).