A proximal-like algorithm for a class of nonconvex programming

Jein Shan Chen, Shaohua Pan

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

In this paper, we study a proximal-like algorithm for minimizing a closed proper function f(x) subject to x30, based on the iterative scheme: xk ε argmin{f(x) + μkd(x, xk-1)}, where d( , ) is an entropy-like distance function. The algorithm is well-defined under the assumption that the problem has a nonempty and bounded solution set. If, in addition, f is a differentiable quasi-convex function (or f is a differentiable function which is homogeneous with respect to a solution), we show that the sequence generated by the algorithm is convergent (or bounded), and furthermore, it converges to a solution of the problem (or every accumulation point is a solution of the problem) when the parameter μk approaches to zero. Preliminary numerical results are also reported, which further verify the theoretical results obtained.

Original languageEnglish
Pages (from-to)319-333
Number of pages15
JournalPacific Journal of Optimization
Volume4
Issue number2
Publication statusPublished - 2008 May 1

Keywords

  • Entropy-like distance
  • Homogeneous
  • Proximal algorithm
  • Quasi-convex

ASJC Scopus subject areas

  • Control and Optimization
  • Computational Mathematics
  • Applied Mathematics

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