An Implementable Proximal Extragradient Method for Structured Fractional Programming

A class of structured fractional programming is studied, where the numerator of the objective function consists of the sum of a nonsmooth function and a smooth function, while the denominator is a convex function. To solve this class of problems, the implementable proximal extragradient algorithm (IPEM) and its variant with linesearch (IPEM-L) are proposed. First, the fractional structure is handled using Dinkelbach’s method. Then, the extended extragradient method is applied to solve the resulting subproblems. By incorporating parameter updates, the proposed algorithms are formulated. A practical linesearch is further introduced to enhance efficiency of the IPEM. Under certain assumptions, both subsequential and whole sequence convergence are established, with the latter relying on the Kurdyka-Łojasiewicz (KŁ) property. Finally, numerical experiments on some synthetic and real datasets demonstrate the competitiveness of the proposed algorithms.