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
The variational inequality problem was introduced as a tool in the study of