Solving Fractional Polynomial Problems by Polynomial Optimization Theory

TL;DR

This paper introduces a polynomial optimization framework to solve fractional polynomial problems, providing a convergent iterative algorithm with proven asymptotic optimality, validated through energy efficiency maximization in MIMO systems.

Contribution

It presents a novel polynomial optimization approach for fractional polynomial problems applicable to a broader class of functions, with a convergent and asymptotically optimal algorithm.

Findings

Algorithm converges reliably in practice.

Validated on energy efficiency maximization in MIMO systems.

Achieves accurate solutions in the non-asymptotic regime.

Abstract

This work aims to introduce the framework of polynomial optimization theory to solve fractional polynomial problems (FPPs). Unlike other widely used optimization frameworks, the proposed one applies to a larger class of FPPs, not necessarily defined by concave and convex functions. An iterative algorithm that is provably convergent and enjoys asymptotic optimality properties is proposed. Numerical results are used to validate its accuracy in the non-asymptotic regime when applied to the energy efficiency maximization in multiuser multiple-input multiple-output communication systems.