Potential reduction method for harmonically convex programming

J. F. Sturm, S. Zhang

Research output: Contribution to journalArticlepeer-review


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 ε-optimal solution is bounded by a polynomial in m, k, and log(1/ε). 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 (US)
Pages (from-to)181-205
Number of pages25
JournalJournal of Optimization Theory and Applications
Issue number1
StatePublished - Jan 1 1995


  • Convex programming
  • harmonic convexity
  • polynomiality
  • potential reduction methods


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