Mixed Max-and-Min Fractional Programming for Wireless Networks

TL;DR

This paper introduces a unified fractional programming framework that handles mixed max-and-min ratio optimization problems in wireless networks, extending existing methods and enabling solutions for complex applications like AoI minimization and secure data rate maximization.

Contribution

It develops a generalized quadratic transform for mixed max-min fractional programming, provides a convergence-guaranteed MM interpretation, and applies the framework to practical wireless network problems.

Findings

Unified approach for mixed max-min fractional programming.

Extended quadratic transform applicable to complex problems.

Effective solutions for AoI minimization and secure data rate maximization.

Abstract

Fractional programming (FP) plays a crucial role in wireless network design because many relevant problems involve maximizing or minimizing ratio terms. Notice that the maximization case and the minimization case of FP cannot be converted to each other in general, so they have to be dealt with separately in most of the previous studies. Thus, an existing FP method for maximizing ratios typically does not work for the minimization case, and vice versa. However, the FP objective can be mixed max-and-min, e.g., one may wish to maximize the signal-to-interference-plus-noise ratio (SINR) of the legitimate receiver while minimizing that of the eavesdropper. We aim to fill the gap between max-FP and min-FP by devising a unified optimization framework. The main results are three-fold. First, we extend the existing max-FP technique called quadratic transform to the min-FP, and further develop a full generalization for the mixed case. Second. we provide a minorization-maximization (MM) interpretation of the proposed unified approach, thereby establishing its convergence and also obtaining a matrix extension; another result we obtain is a generalized Lagrangian dual transform which facilitates the solving of the logarithmic FP. Finally, we present three typical applications: the age-of-information (AoI) minimization, the Cramer-Rao bound minimization for sensing, and the secure data rate maximization, none of which can be efficiently addressed by the previous FP methods.