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

S. H. Pan, J. S. Chen

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

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 ℝ++. Since the distance function has some favorable properties similar to those of the D-function (Censor and Zenios in J. Optim. Theory Appl. 73:451-464 [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. 73:451-464 [1992]; Chen and Teboulle in SIAM J. Optim. 3:538-543 [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 proposed algorithm is bounded and that every accumulation point is a solution to the considered problem.

Original languageEnglish
Pages (from-to)95-113
Number of pages19
JournalJournal of Optimization Theory and Applications
Volume138
Issue number1
DOIs
Publication statusPublished - 2008 Jul 1

Keywords

  • Bregman functions
  • Convex second-order cone programming
  • Proximal-like methods
  • Quasi D-functions

ASJC Scopus subject areas

  • Control and Optimization
  • Management Science and Operations Research
  • Applied Mathematics

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