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REFORMULATION OF VARIATIONAL INEQUALITIES ON A SIMPLEX AND COMPACTIFICATION OF
 

Summary: REFORMULATION OF VARIATIONAL INEQUALITIES
ON A SIMPLEX AND COMPACTIFICATION OF
COMPLEMENTARITY PROBLEMS
ROBERTO ANDREANI AND JOS´E MARIO MART´INEZ
SIAM J. OPTIM. c 2000 Society for Industrial and Applied Mathematics
Vol. 10, No. 3, pp. 878­895
Abstract. Many variational inequality problems (VIPs) can be reduced, by a compactifica-
tion procedure, to a VIP on the canonical simplex. Reformulations of this problem are studied,
including smooth reformulations with simple constraints and unconstrained reformulations based
on the penalized Fischer­Burmeister function. It is proved that bounded level set results hold for
these reformulations under quite general assumptions on the operator. Therefore, it can be guaran-
teed that minimization algorithms generate bounded sequences and, under monotonicity conditions,
these algorithms necessarily find solutions of the original problem. Some numerical experiments are
presented.
Key words. variational inequalities, complementarity, minimization algorithms, reformulation
AMS subject classifications. 90C33, 90C30
PII. S1052623499352826
1. Introduction. We are interested in reformulations of variational inequality
problems (VIPs) where the domain is a simplex. The main motivation is that varia-
tional inequalities on generalized (perhaps unbounded) boxes can be reduced to the

  

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

 

Collections: Mathematics