A proximal point algorithm for the monotone second-order cone complementarity problem |
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Authors: | Jia Wu Jein-Shan Chen |
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Institution: | 1.School of Mathematical Sciences,Dalian University of Technology,Dalian,China;2.Department of Mathematics,National Taiwan Normal University,Taipei,Taiwan |
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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. |
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Keywords: | |
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