Merit Functions and Descent Algorithms for a Class of Variational Inequality
Problems

Michael Patriksson

Division of Optimization 
Department of Mathematics 
Linköping Institute of Technology
S-581 83 Linköping 
Sweden

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 (1989), 
and the descent algorithms are likewise generalizations of those of 
Fukushima (1992), Larsson and Patriksson (1994) and several others, for 
variational inequality problems with single-valued cost mappings.

KEY WORDS: Variational Inequality Problems, Set-Valued Mappings, Merit Functions, 
Variational Principles, Fenchel's Inequality, Cost Approximation, 
Descent Algorithms