Solving Fractional Polynomial Problems by Polynomial Optimization Theory

This letter aims at introducing 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/or 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 nonasymptotic regime when applied to the energy efficiency maximization in multiuser multiple-input multiple-output communication systems.