## 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 language | English |
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Pages (from-to) | 181-205 |

Number of pages | 25 |

Journal | Journal of optimization theory and applications |

Volume | 84 |

Issue number | 1 |

Publication status | Published - Jan-1995 |

## Keywords

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