On the identification of degenerate indices in the nonlinear complementarity problem with the proximal point algorithm

• 成果类型: Article
• 署名作者: Yamashita, N; Dan, H; Fukushima, M
• 署名单位: Kyoto University
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-003-0455-x
• 发表日期: 2004
• 页码: 377-397
• 关键词: newton methods; zero variables; error-bounds; equation

摘要

In this paper we focus on the problem of identifying the index sets P(x) := {i \ x(i)>0}, N(x) := {i \ F-i(x)>0} and C(x) := {i \ x(i) = F-i(x)=0} for a solution x of the monotone nonlinear complementarity problem NCP(F). The correct identification of these sets is important from both theoretical and practical points of view. Such an identification enables us to remove complementarity conditions from the NCP and locally reduce the NCP to a system which can be dealt with more easily. We present a new technique that utilizes a sequence generated by the proximal point algorithm (PPA). Using the superlinear convergence property of PPA, we show that the proposed technique can identify the correct index sets without assuming the nondegeneracy and the local uniqueness of the solution.