Controlled dual perturbations for central path trajectories in geometric programming

Abstract

A dynamic perturbation algorithm is developed building on the work of Fang, Peterson and Rajasekera, who introduced simple lower bounds as perturbations in an equivalent dual pair to the posynomial geometric programming primal and dual programs. In their approach, a duality gap tolerance is pre-specified, and then the perturbations are determined from additional information, such as a current feasible point and a bound for the optimal program value. Our approach updates the perturbation vector in at most O(In ϵ) outer loop iterations, while requiring no more than a 50% reduction in the current duality gap in each inner loop iteration. One of the advantages of our approach is that the perturbation bound tends to stay away from zero in a way that results in more stable computations.