A damped Gauss-Newton method for the second-order cone complementarity problem

Shaohua Pan Jein-Shan Chen

Optimization and Control mathscidoc:1910.43873

Applied Mathematics and Optimization, 59, (3), 293, 2009.6
We investigate some properties related to the generalized Newton method for the Fischer-Burmeister (FB) function over second-order cones, which allows us to reformulate the second-order cone complementarity problem (SOCCP) as a semismooth system of equations. Specifically, we characterize the B-subdifferential of the FB function at a general point and study the condition for every element of the B-subdifferential at a solution being nonsingular. In addition, for the induced FB merit function, we establish its coerciveness and provide a weaker condition than Chen and Tseng (Math. Program. 104:293327, 2005) for each stationary point to be a solution, under suitable Cartesian <i>P</i>-properties of the involved mapping. By this, a damped Gauss-Newton method is proposed, and the global and superlinear convergence results are obtained. Numerical results are reported for the second-order cone programs
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@inproceedings{shaohua2009a,
  title={A damped Gauss-Newton method for the second-order cone complementarity problem},
  author={Shaohua Pan, and Jein-Shan Chen},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020223207469342402},
  booktitle={Applied Mathematics and Optimization},
  volume={59},
  number={3},
  pages={293},
  year={2009},
}
Shaohua Pan, and Jein-Shan Chen. A damped Gauss-Newton method for the second-order cone complementarity problem. 2009. Vol. 59. In Applied Mathematics and Optimization. pp.293. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020223207469342402.
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