Indexed by:期刊论文

Date of Publication:2009-01-01

Journal:NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS

Included Journals:SCIE、EI、Scopus

Volume:70

Issue:1

Page Number:211-219

ISSN No.:0362-546X

Key Words:Variational inequality; Smoothing method; Homotopy method; Global convergence

Abstract:In this paper, a new homotopy method for solving the variational inequality problem VIP(X, F): find y* is an element of X such that (y - y*)(T) F(y*) >= 0, for all y is an element of X, where X is a nonempty closed convex subset of R(n) and F : R(n) --> R(n) is a continuously differentiable mapping, is proposed. The homolopy equation is constructed based on the smooth approximation to Robinson's normal equation of variational inequality problem, where the smooth approximation function p(x, A) of the projection function Pi(X)(x) is an arbitrary one such that for any mu > 0 and x is an element of R(n), p(x, mu) is an element of int X. Under a weak condition on the defining mapping F, which is needed for the existence of a solution to VIP(X, F), for the starting point chosen almost everywhere in R(n), existence and convergence of a smooth homotopy pathway to a solution of VIP(X, F) are proved. Several numerical experiments indicate that the method is efficient. (C) 2007 Elsevier Ltd. All rights reserved.