Hits:

Date:2019-03-09

Indexed by:Journal Article

Date of Publication:2012-04-01

Journal:COMPUTATIONAL OPTIMIZATION AND APPLICATIONS

Included Journals:EI、SCIE

Volume:51

Issue:3

Page Number:1037-1063

ISSN:0926-6003

Key Words:Complementarity problem; Second-order cone; Proximal point algorithm; Approximation criterion

Abstract:This paper is devoted to the study of the proximal point algorithm for solving monotone second-order cone complementarity problems. The proximal point algorithm is to generate a sequence by solving subproblems that are regularizations of the original problem. After given an appropriate criterion for approximate solutions of subproblems by adopting a merit function, the proximal point algorithm is verified to have global and superlinear convergence properties. For the purpose of solving the subproblems efficiently, we introduce a generalized Newton method and show that only one Newton step is eventually needed to obtain a desired approximate solution that approximately satisfies the appropriate criterion under mild conditions. Numerical comparisons are also made with the derivative-free descent method used by Pan and Chen (Optimization 59:1173-1197, 2010), which confirm the theoretical results and the effectiveness of the algorithm.