POTENTIAL REDUCTION METHOD FOR HARMONICALLY CONVEX-PROGRAMMING

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.