On the Construction of an Approximate Optimal Solution for Geometric Programming Problem

Abstract

This paper concerns with an approximate optimization technique of geometric programming (GP). The optimal solution is obtained by solving the dual problem which is derived from the given primal problem. And the calculation volume to solve the dual problem is measured by the term called “degree of difficulty”.
Until now, we already proposed a method to calculate an approximate optimum of GP problem. But, the approximate optimal solution corresponding to the approximate optimum is not obtained.
In this paper, next two results are shown, namely, i) the construction method of an approximate optimal solution and ii) an inequality which can be used to estimate the difference between the approximate optimum and the objective function value at the approximate optimal solution. This inequalty includes the decomposition gain, which is introduced here and can be used to judge whether the approximate optimal solution is good or not. At last some numerical examples are shown to illustrate the above results.