An unconstrained smooth minimization reformulation of the second-order cone complementarity problem

Jein-Shan Chen Paul Tseng

Optimization and Control mathscidoc:1910.43870

Mathematical Programming, 104, 293-327, 2005.11
A popular approach to solving the nonlinear complementarity problem (NCP) is to reformulate it as the global minimization of a certain merit function over <sup> <i>n</i> </sup>. A popular choice of the merit function is the squared norm of the Fischer-Burmeister function, shown to be smooth over <sup> <i>n</i> </sup> and, for monotone NCP, each stationary point is a solution of the NCP. This merit function and its analysis were subsequently extended to the semidefinite complementarity problem (SDCP), although only differentiability, not continuous differentiability, was established. In this paper, we extend this merit function and its analysis, including continuous differentiability, to the second-order cone complementarity problem (SOCCP). Although SOCCP is reducible to a SDCP, the reduction does not allow for easy translation of the analysis from SDCP to SOCCP. Instead, our analysis exploits
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@inproceedings{jein-shan2005an,
  title={An unconstrained smooth minimization reformulation of the second-order cone complementarity problem},
  author={Jein-Shan Chen, and Paul Tseng},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020223122572166399},
  booktitle={Mathematical Programming},
  volume={104},
  pages={293-327},
  year={2005},
}
Jein-Shan Chen, and Paul Tseng. An unconstrained smooth minimization reformulation of the second-order cone complementarity problem. 2005. Vol. 104. In Mathematical Programming. pp.293-327. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020223122572166399.
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