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A linearly convergent derivative-free descent method for the second-order cone complementarity problem

Shaohua Pan Jein-Shan Chen

Optimization and Control mathscidoc:1910.43903

Optimization, 59, (8), 1173-1197, 2010.11
We consider a class of derivative-free descent methods for solving the second-order cone complementarity problem (SOCCP). The algorithm is based on the FischerBurmeister (FB) unconstrained minimization reformulation of the SOCCP, and utilizes a convex combination of the negative partial gradients of the FB merit function <sub>FB</sub> as the search direction. We establish the global convergence results of the algorithm under monotonicity and the uniform Jordan <i>P</i>-property, and show that under strong monotonicity the merit function value sequence generated converges at a linear rate to zero. Particularly, the rate of convergence is dependent on the structure of second-order cones. Numerical comparisons are also made with the limited BFGS method used by Chen and Tseng (<i>An unconstrained smooth minimization reformulation of the second-order cone complementarity problem</i>, Math. Program. 104(2005), pp
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@inproceedings{shaohua2010a,
  title={A linearly convergent derivative-free descent method for the second-order cone complementarity problem},
  author={Shaohua Pan, and Jein-Shan Chen},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020224223122491432},
  booktitle={Optimization},
  volume={59},
  number={8},
  pages={1173-1197},
  year={2010},
}
Shaohua Pan, and Jein-Shan Chen. A linearly convergent derivative-free descent method for the second-order cone complementarity problem. 2010. Vol. 59. In Optimization. pp.1173-1197. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020224223122491432.
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