Summary: Bound Constrained Smooth Optimization for Solving
Variational Inequalities and Related Problems.
Roberto Andreani # Ana Friedlander +
July 26, 2002
Abstract
Variational inequalities and related problems may be solved via smooth bound
constrained optimization. A comprehensive discussion of the important features in­
volved with this strategy is presented. Complementarity problems and mathematical
programming problems with equilibrium constraints are included in this report. Nu­
merical experiments are commented. Conclusions and directions of future research are
indicated.
Keywords. Bound constrained optimization, variational inequalities, merit functions.
AMS: 90C33, 90C30
1 Introduction
Various reformulations of the variational inequality problem (VIP) in finite dimensional
spaces as optimization problems have been proposed in the last ten years. In this paper
# Department of Computer Science and Statistics, University of the State of S. Paulo (UNESP), CEP
15054­000, S”ao Jos’e do Rio Preto­SP, Brazil. This author was supported by FAPESP (Grant 99/08381­4)
and CNPq (Grant 301115/96­6). E­mail: andreani@dcce.ibilce.unesp.br
+ Department of Applied Mathematics, IMECC­UNICAMP, University of Campinas, CP 6065, 13081­

Source: Andreani, Roberto - Instituto de Matemática, Estatística e Computação Científica, Universidade Estadual de Campinas

Collections: Mathematics