Entropy-like proximal algorithms based on a second-order homogeneous distance function for quasi-convex programming

Shaohua Pan, Jein-Shan Chen

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

We consider two classes of proximal-like algorithms for minimizing a proper lower semicontinuous quasi-convex function f(x) subject to non-negative constraints x ≥ 0. The algorithms are based on an entropy-like second-order homogeneous distance function. Under the assumption that the global minimizer set is nonempty and bounded, we prove the full convergence of the sequence generated by the algorithms, and furthermore, obtain two important convergence results through imposing certain conditions on the proximal parameters. One is that the sequence generated will converge to a stationary point if the proximal parameters are bounded and the problem is continuously differentiable, and the other is that the sequence generated will converge to a solution of the problem if the proximal parameters approach to zero. Numerical experiments are done for a class of quasi-convex optimization problems where the function f(x) is a composition of a quadratic convex function from Rn to R and a continuously differentiable increasing function from R to R, and computational results indicate that these algorithms are very promising in finding a global optimal solution to these quasi-convex problems.

Original languageEnglish
Pages (from-to)555-575
Number of pages21
JournalJournal of Global Optimization
Volume39
Issue number4
DOIs
Publication statusPublished - 2007 Dec 1

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Quasiconvex Programming
Proximal Algorithm
Homogeneous Function
Convex optimization
Distance Function
entropy
Entropy
Quasiconvex
Continuously differentiable
Converge
Quasiconvex Functions
Lower Semicontinuous Function
Global Minimizer
Increasing Functions
Stationary point
Quadratic Function
Convex Optimization
Convergence Results
Convex function
Computational Results

Keywords

  • Entropy-like distance
  • Proximal-like method
  • Quasi-convex programming

ASJC Scopus subject areas

  • Applied Mathematics
  • Control and Optimization
  • Management Science and Operations Research
  • Global and Planetary Change

Cite this

Entropy-like proximal algorithms based on a second-order homogeneous distance function for quasi-convex programming. / Pan, Shaohua; Chen, Jein-Shan.

In: Journal of Global Optimization, Vol. 39, No. 4, 01.12.2007, p. 555-575.

Research output: Contribution to journalArticle

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