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

Shaohua Pan, Jein Shan Chen

研究成果: 雜誌貢獻文章

8 引文 斯高帕斯(Scopus)

摘要

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, +00), and includes as a special case the entropy-like proximal algorithm [Eggermont, Linear Algebra Appl., 130 (1990), pp. 25-42], 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 sequence generated is bounded, and every accumulation point is a solution of the considered problem. Preliminary numerical results are reported for two approximate entropy-like proximal algorithms, and numerical comparisons are also made with the merit function approach [Chen and Tseng, Math. Program., 104 (2005), pp. 293-327], which verify the effectiveness of the proposed method.

原文英語
頁(從 - 到)883-910
頁數28
期刊SIAM Journal on Optimization
19
發行號2
DOIs
出版狀態已發佈 - 2008 六月 1

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science

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