A parameter-free approach for solving SOS-convex semi-algebraic fractional programs

TL;DR

This paper introduces a parameter-free method for solving SOS-convex semi-algebraic fractional programs, establishing strong duality and enabling extraction of optimal solutions via a single SDP relaxation.

Contribution

It presents a novel parameter-free approach with strong duality results and a practical method to obtain solutions from a single SDP relaxation for this class of problems.

Findings

Strong duality between the fractional program and SDP relaxations.

Optimal solutions can be extracted from one SDP problem.

Numerical examples demonstrate the effectiveness of the approach.

Abstract

In this paper, we study a class of nonsmooth fractional programs {\rm (FP, for short)} with SOS-convex semi-algebraic functions. Under suitable assumptions, we derive a strong duality result between the problem (FP) and its semidefinite programming (SDP) relaxations. Remarkably, we extract an optimal solution of the problem (FP) by solving one and only one associated SDP problem. Numerical examples are also given.