Summary: Solution of Finite­Dimensional Variational
Inequalities Using Smooth Optimization with
Simple Bounds 1
R. Andreani, 2 A. Friedlander 3 and J. M. Mart' inez 4
1 This work was supported by FAPESP, Grants 90­3724­6 and 93­2479­6, CNPq, FINEP
and FAEP­UNICAMP.
2 Graduate Student, Department of Applied Mathematics, IMECC­UNICAMP, Uni­
versity of Campinas, Campinas, SP, Brazil.
3 Associate Professor, Department of Applied Mathematics, IMECC­UNICAMP, Uni­
versity of Campinas, Campinas, SP, Brazil.
4
Full Professor, Department of Applied Mathematics, IMECC­UNICAMP, University
of Campinas, Campinas, SP, Brazil.

Abstract. The variational inequality problem is reduced to an optimization
problem with a differentiable objective function and simple bounds. Theo­
retical results are proved, that relate stationary points of the minimization
problem to solutions of the variational inequality problem. Perturbations
of the original problem are studied and an algorithm that uses the smooth
minimization approach for solving monotone problems is defined.

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

Collections: Mathematics