A merit function method for infinite-dimensional SOCCPs

Yungyen Chiang Shaohua Pan Jein-Shan Chen

Functional Analysis mathscidoc:1910.43911

Journal of Mathematical Analysis and Applications, 383, (1), 159-178, 2011.11
We introduce the Jordan product associated with the second-order cone K into the real Hilbert space H, and then define a one-parametric class of complementarity functions t on H H with the parameter t[0, 2). We show that the squared norm of t with t(0, 2) is a continuously F (rchet)-differentiable merit function. By this, the second-order cone complementarity problem (SOCCP) in H can be converted into an unconstrained smooth minimization problem involving this class of merit functions, and furthermore, under the monotonicity assumption, every stationary point of this minimization problem is shown to be a solution of the SOCCP.
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@inproceedings{yungyen2011a,
  title={A merit function method for infinite-dimensional SOCCPs},
  author={Yungyen Chiang, Shaohua Pan, and Jein-Shan Chen},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020224544453189440},
  booktitle={Journal of Mathematical Analysis and Applications},
  volume={383},
  number={1},
  pages={159-178},
  year={2011},
}
Yungyen Chiang, Shaohua Pan, and Jein-Shan Chen. A merit function method for infinite-dimensional SOCCPs. 2011. Vol. 383. In Journal of Mathematical Analysis and Applications. pp.159-178. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020224544453189440.
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