Exponential Conic Relaxations for Signomial Geometric Programming

TL;DR

This paper introduces a new convex relaxation technique for signomial geometric programming that leverages exponential conic programming advances, improving solution strength without variable bounds, and demonstrates practical effectiveness through experiments.

Contribution

It develops a novel unbounded-variable convex relaxation for SGP using exponential conic programming, enhancing iterative solution methods.

Findings

Effective relaxation without bounded variables

Improved iterative solution approach

Demonstrated computational efficiency

Abstract

Signomial geometric programming (SGP) is a computationally challenging, NP-Hard class of nonconvex nonlinear optimization problems. SGP can be solved iteratively using a sequence of convex relaxations; consequently, the strength of such relaxations is an important factor to this iterative approach. Motivated by recent advances in solving exponential conic programming (ECP) problems, this paper develops a novel convex relaxation for SGP. Unlike existing work on relaxations, the base model in this paper does not assume bounded variables. However, bounded variables or monomial terms can be used to strengthen the relaxation by means of additional valid linear inequalities. We show how to embed the ECP relaxation in an iterative algorithm for SGP; leveraging recent advances in interior point method solvers, our computational experiments demonstrate the practical effectiveness of this approach.