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

Jia Wu Jein-Shan Chen

Optimization and Control mathscidoc:1910.43931

Computational Optimization and Applications, 51, (3), 1037-1063, 2012.4
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 59:11731197, 2010), which confirm the theoretical results
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@inproceedings{jia2012a,
  title={A proximal point algorithm for the monotone second-order cone complementarity problem},
  author={Jia Wu, and Jein-Shan Chen},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020225142854981460},
  booktitle={Computational Optimization and Applications},
  volume={51},
  number={3},
  pages={1037-1063},
  year={2012},
}
Jia Wu, and Jein-Shan Chen. A proximal point algorithm for the monotone second-order cone complementarity problem. 2012. Vol. 51. In Computational Optimization and Applications. pp.1037-1063. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020225142854981460.
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