An entropy-like proximal algorithm and the exponential multiplier method for convex symmetric cone programming

Jein-Shan Chen, Shaohua Pan

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

We introduce an entropy-like proximal algorithm for the problem of minimizing a closed proper convex function subject to symmetric cone constraints. The algorithm is based on a distance-like function that is an extension of the Kullback- Leiber relative entropy to the setting of symmetric cones. Like the proximal algorithms for convex programming with nonnegative orthant cone constraints, we show that, under some mild assumptions, the sequence generated by the proposed algorithm is bounded and every accumulation point is a solution of the considered problem. In addition, we also present a dual application of the proposed algorithm to the symmetric cone linear program, leading to a multiplier method which is shown to possess similar properties as the exponential multiplier method (Tseng and Bertsekas in Math. Program. 60:1-19, 1993) holds.

Original languageEnglish
Pages (from-to)477-499
Number of pages23
JournalComputational Optimization and Applications
Volume47
Issue number3
DOIs
Publication statusPublished - 2010 Nov 1

Fingerprint

Proximal Algorithm
Symmetric Cone
Multiplier Method
Convex Cone
Cone Constraints
Cones
Entropy
Programming
Accumulation point
Relative Entropy
Convex Programming
Linear Program
Convex function
Non-negative
Convex optimization
Closed

Keywords

  • Entropy-like distance
  • Exponential multiplier method
  • Proximal-like method
  • Symmetric cone optimization

ASJC Scopus subject areas

  • Control and Optimization
  • Computational Mathematics
  • Applied Mathematics

Cite this

An entropy-like proximal algorithm and the exponential multiplier method for convex symmetric cone programming. / Chen, Jein-Shan; Pan, Shaohua.

In: Computational Optimization and Applications, Vol. 47, No. 3, 01.11.2010, p. 477-499.

Research output: Contribution to journalArticle

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