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

Shaohua Pan, Jein-Shan Chen

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)883-910
Number of pages28
JournalSIAM Journal on Optimization
Volume19
Issue number2
DOIs
Publication statusPublished - 2008 Jun 1

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Proximal Algorithm
Convex Order
Second-order Cone Programming
Convex Programming
Convex Cone
Convex function
Second-order Cone
Cones
Interior
Non-negative
Entropy
Approximate Entropy
Cone Constraints
Merit Function
Accumulation point
Continuously differentiable
Numerical Comparisons
Strictly Convex
Distance Measure
Global Convergence

Keywords

  • Measure of distance
  • Proximal method
  • Second-order cone
  • Second-order cone-convexity

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science

Cite this

A class of interior proximal-like algorithms for convex second-order cone programming. / Pan, Shaohua; Chen, Jein-Shan.

In: SIAM Journal on Optimization, Vol. 19, No. 2, 01.06.2008, p. 883-910.

Research output: Contribution to journalArticle

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