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A class of interior proximal-like algorithms for convex second-order cone programming

Shaohua Pan Jein-Shan Chen

Optimization and Control mathscidoc:1910.43898

SIAM Journal on Optimization, 19, (2), 883-910, 2008.8
We propose a class of interior proximal-like algorithms for the second-order cone program, which is to minimize a closed proper convex function subject to general second-order cone constraints. The class of methods uses a distance measure generated by a twice continuously differentiable strictly convex function on (0,+\infty), and includes as a special case the entropy-like proximal algorithm [Eggermont, <i>Linear Algebra Appl.</i>, 130 (1990), pp. 2542], which was originally proposed for minimizing a convex function subject to nonnegative constraints. Particularly, we consider an approximate version of these methods, allowing the inexact solution of subproblems. Like the entropy-like proximal algorithm for convex programming with nonnegative constraints, we, under some mild assumptions, establish the global convergence expressed in terms of the objective values for the proposed algorithm, and we show that the
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@inproceedings{shaohua2008a,
  title={A class of interior proximal-like algorithms for convex second-order cone programming},
  author={Shaohua Pan, and Jein-Shan Chen},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020224054902213427},
  booktitle={SIAM Journal on Optimization},
  volume={19},
  number={2},
  pages={883-910},
  year={2008},
}
Shaohua Pan, and Jein-Shan Chen. A class of interior proximal-like algorithms for convex second-order cone programming. 2008. Vol. 19. In SIAM Journal on Optimization. pp.883-910. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020224054902213427.
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