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 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 language | English (US) |
|---|---|
| Pages (from-to) | 181-205 |
| Number of pages | 25 |
| Journal | Journal of Optimization Theory and Applications |
| Volume | 84 |
| Issue number | 1 |
| DOIs | |
| State | Published - Jan 1 1995 |
Keywords
- Convex programming
- harmonic convexity
- polynomiality
- potential reduction methods