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Proximal-like algorithm using the quasi D-function for convex second-order cone programming

SH Pan Jein-Shan Chen

Numerical Analysis and Scientific Computing mathscidoc:1910.43909

Journal of Optimization Theory and Applications, 138, (1), 95, 2008.7
In this paper, we present a measure of distance in a second-order cone based on a class of continuously differentiable strictly convex functions on <sub>++</sub>. Since the distance function has some favorable properties similar to those of the D-function (Censor and Zenios in J. Optim. Theory Appl. 73:451464 [1992]), we refer to it as a quasi D-function. Then, a proximal-like algorithm using the quasi D-function is proposed and applied to the second-cone programming problem, which is to minimize a closed proper convex function with general second-order cone constraints. Like the proximal point algorithm using the D-function (Censor and Zenios in J. Optim. Theory Appl. 73:451464 [1992]; Chen and Teboulle in SIAM J. Optim. 3:538543 [1993]), under some mild assumptions we establish the global convergence of the algorithm expressed in terms of function values; we show that the sequence generated by the
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@inproceedings{sh2008proximal-like,
  title={Proximal-like algorithm using the quasi D-function for convex second-order cone programming},
  author={SH Pan, and Jein-Shan Chen},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020224431367290438},
  booktitle={Journal of Optimization Theory and Applications},
  volume={138},
  number={1},
  pages={95},
  year={2008},
}
SH Pan, and Jein-Shan Chen. Proximal-like algorithm using the quasi D-function for convex second-order cone programming. 2008. Vol. 138. In Journal of Optimization Theory and Applications. pp.95. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020224431367290438.
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