A descent method for a reformulation of the second-order cone complementarity problem

Jein-Shan Chen Shaohua Pan

Optimization and Control mathscidoc:1910.43888

Journal of Computational and Applied Mathematics, 213, (2), 547-558, 2008.4
Analogous to the nonlinear complementarity problem and the semi-definite complementarity problem, a popular approach to solving the second-order cone complementarity problem (SOCCP) is to reformulate it as an unconstrained minimization of a certain merit function over R n. In this paper, we present a descent method for solving the unconstrained minimization reformulation of the SOCCP which is based on the FischerBurmeister merit function (FBMF) associated with second-order cone [J.-S. Chen, P. Tseng, An unconstrained smooth minimization reformulation of the second-order cone complementarity problem, Math. Programming 104 (2005) 293327], and prove its global convergence. Particularly, we compare the numerical performance of the method for the symmetric affine SOCCP generated randomly with the FBMF approach [J.-S. Chen, P. Tseng, An unconstrained smooth minimization reformulation
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@inproceedings{jein-shan2008a,
  title={A descent method for a reformulation of the second-order cone complementarity problem},
  author={Jein-Shan Chen, and Shaohua Pan},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020223758467470417},
  booktitle={Journal of Computational and Applied Mathematics},
  volume={213},
  number={2},
  pages={547-558},
  year={2008},
}
Jein-Shan Chen, and Shaohua Pan. A descent method for a reformulation of the second-order cone complementarity problem. 2008. Vol. 213. In Journal of Computational and Applied Mathematics. pp.547-558. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020223758467470417.
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