Merit functions and descent algorithms for a class of variational inequality problems

Abstract. We consider a variational inequality problem, where the cost mapping is the sum of a single-valued mapping and the subdifferential mapping of a convex function. For this problem we introduce a new class of equivalent optimization formulations; based on them, we also provide the first convergence analysis of descent algorithms for the problem. The optimization formulations constitute generalizations of those presented by Auchmuty [Auc89], and the descent algorithms are likewise generalizations of those of Fukushima [Fuk92], Larsson and Patriksson [LaP94] and several others, for variational inequality problems with single-valued cost mappings