TY - JOUR

T1 - A proximal point algorithm for the monotone second-order cone complementarity problem

AU - Wu, Jia

AU - Chen, Jein Shan

N1 - Funding Information:
J.-S. Chen is a member of Mathematics Division, National Center for Theoretical Sciences, Taipei Office. The author’s work is partially supported by National Science Council of Taiwan.

PY - 2012/4

Y1 - 2012/4

N2 - 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.

AB - 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.

KW - Approximation criterion

KW - Complementarity problem

KW - Proximal point algorithm

KW - Second-order cone

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U2 - 10.1007/s10589-011-9399-x

DO - 10.1007/s10589-011-9399-x

M3 - Article

AN - SCOPUS:84862017728

SN - 0926-6003

VL - 51

SP - 1037

EP - 1063

JO - Computational Optimization and Applications

JF - Computational Optimization and Applications

IS - 3

ER -