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ON THE RESOLUTION OF THE GENERALIZED NONLINEAR COMPLEMENTARITY PROBLEM #
 

Summary: ON THE RESOLUTION OF THE GENERALIZED NONLINEAR
COMPLEMENTARITY PROBLEM #
ROBERTO ANDREANI + , ANA FRIEDLANDER # , AND SANDRA A. SANTOS #
SIAM J. OPTIM. c
# 2001 Society for Industrial and Applied Mathematics
Vol. 12, No. 2, pp. 303--321
Abstract. Minimization of a di#erentiable function subject to box constraints is proposed as a
strategy to solve the generalized nonlinear complementarity problem (GNCP) defined on a polyhedral
cone. It is not necessary to calculate projections that complicate and sometimes even disable the
implementation of algorithms for solving these kinds of problems. Theoretical results that relate
stationary points of the function that is minimized to the solutions of the GNCP are presented.
Perturbations of the GNCP are also considered, and results are obtained related to the resolution
of GNCPs with very general assumptions on the data. These theoretical results show that local
methods for box­constrained optimization applied to the associated problem are e#cient tools for
solving the GNCP. Numerical experiments are presented that encourage the use of this approach.
Key words. box­constrained optimization, complementarity
AMS subject classifications. 65H10, 90C33, 90C30
PII. S1052623400377591
1. Introduction. The generalized nonlinear complementarity problem (GNCP)
is to find x # R m such that

  

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

 

Collections: Mathematics