Proximal bundle methods for generalized fractional programs with ratios of difference of convex functions

¹ Laboratory of Applied Mathematics and Scientific Computing, Higher School of Education and Training, Sultan Moulay Slimane University, P.O. Box 523, Béni Mellal 23000, Morocco
² Hassan First University of Settat, Faculté des Sciences et Techniques, Laboratoire MDSET, Settat 26000, Morocco

^* Corresponding author: ghaziab@hotmail.com

Received: 23 September 2024
Accepted: 17 May 2025

Abstract

In this paper, we present an approximating scheme based on the proximal point algorithm for solving generalized fractional programs involving ratios of difference of convex (DC) functions and subject to DC constraints, which we shall refer to as DC-GFP. These problems are usually nonsmooth and nonconvex, but we approximate them iteratively with parametric convex ones. We capitalize on the latter attribute to employ the conventional bundle method to address them. The proposed method is seen as a pure proximal algorithm or a proximal bundle method and generates a sequence of approximate solutions that converge to critical points satisfying the necessary optimality conditions of the KKT type. Finally, we provide numerical test results to illustrate the effectiveness of our algorithm.