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On the regularization of mixed complementarity R. Andreani \Lambda J. M. Mart'inez y B. F. Svaiter z

Summary: On the regularization of mixed complementarity
R. Andreani \Lambda J. M. Mart'inez y B. F. Svaiter z
November 8, 1999
A variational inequality problem (VIP) satisfying a constraint qual­
ification can be reduced to a mixed complementarity problem (MCP).
Monotonicity of the VIP implies that the MCP is also monotone. In­
troducing regularizing perturbations, a sequence of strictly monotone
mixed complementarity problems are generated. It is shown that, if
the original problem is solvable, the sequence of computable inexact
solutions of the strictly monotone MCP's is bounded and every accu­
mulation point is a solution. Under an additional condition on the
precision used for solving each subproblem, the sequence converges to
the minimum norm solution of the MCP.
Keywords. Variational inequalities, complementarity, perturbations,
inexact solutions, minimization algorithms, reformulation.
AMS: 90C33, 90C30
1 Introduction
The variational inequality problem was introduced as a tool in the study of


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


Collections: Mathematics