POTENTIAL REDUCTION METHOD FOR HARMONICALLY CONVEX-PROGRAMMING

JF STURM*, S ZHANG

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

In this paper, we introduce a potential reduction method for harmonically convex programming. We show that, if the objective function and the m constraint functions are all k-harmonically convex in the feasible set, then the number of iterations needed to find an is-an-element-of-optimal solution is bounded by a polynomial in m, k, and log(1/is-an-element-of). The method requires either the optimal objective value of the problem or an upper bound of the harmonic constant k as a working parameter. Moreover, we discuss the relation between the harmonic convexity condition used in this paper and some other convexity and smoothness conditions used in the literature.

Original languageEnglish
Pages (from-to)181-205
Number of pages25
JournalJournal of optimization theory and applications
Volume84
Issue number1
Publication statusPublished - Jan-1995

Keywords

  • CONVEX PROGRAMMING
  • HARMONIC CONVEXITY
  • POTENTIAL REDUCTION METHODS
  • POLYNOMIALITY
  • POLYNOMIAL-TIME ALGORITHM

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