An Efficient Algorithm for Solving a Class of Fractional Programming Problems

Abstract

This paper presents an efficient branch-and-bound algorithm for globally solving a class of fractional programming problems, which are widely used in communication engineering, financial engineering, portfolio optimization, and other fields. Since the kind of fractional programming problems is nonconvex, in which multiple locally optimal solutions generally exist that are not globally optimal, so there are some vital theoretical and computational difficulties. In this paper, first of all, for constructing this algorithm, we propose a novel linearizing method so that the initial fractional programming problem can be converted into a linear relaxation programming problem by utilizing the linearizing method. Secondly, based on the linear relaxation programming problem, a novel branch-and-bound algorithm is designed for the kind of fractional programming problems, the global convergence of the algorithm is proved, and the computational complexity of the algorithm is analysed. Finally, numerical results are reported to indicate the feasibility and effectiveness of the algorithm.

Application of Linear Programming to Optimize Sugarcane Production and Sugarcane Farming Income at HGU Jengkol PT. Perkebunan Nusantara X

“…Furthermore, the application of linear programming extends to fields such as biotechnology, where it has been used in the development of reliable simulators for dynamic flux balance analysis, integrating genome-scale metabolic network analysis with dynamic simulation of the extracellular environment (Höffner et al, 2012). In the realm of mathematics, linear programming has been employed in solving fractional programming problems, with algorithms proposed for efficient solutions to specific forms of fractional programming problems (Qiu et al, 2021). Additionally, the application of linear programming in semi-infinite programming has been explored, with sensitivity analysis conducted via partitions, extending the concept of optimal partition from ordinary to semi-infinite linear programming (Goberna et al, 2010).…”