An Efficient Algorithm for Quadratic Sum-of-Ratios Fractional Programs Problem. (2nd November 2017)

• Record Type: Journal Article
• Authors: Jiao, Hongwei; Liu, Sanyang
• Is Part Of: Numerical functional analysis and optimization. Volume 38:Number 11(2017)
• Page Start: 1426
• Page End: 1445
• Publication Date: 2017-11-02
• Subjects: Branch-and-bound -- fractional programs -- global optimization -- parametric linearizing technique -- quadratic sum-of-ratios; 90C30 -- 90C32 -- 65K05; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2017.1327869
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: The quadratic sum-of-ratios fractional program problem has a broad range of applications in practical problems. This article will present an efficient branch-and-bound algorithm for globally solving the quadratic sum-of-ratios fractional program problem. In this algorithm, lower bounds are computed by solving a series of parametric relaxation linear programming problems, which are established by utilizing new parametric linearizing technique. To enhance the computational speed of the proposed algorithm, a rectangle reducing tactic is used to reject a part of the investigated rectangle or the whole rectangle where there does not contain any global optimal solution of the quadratic sum-of-ratios fractional program problem. Compared with the known approaches, the proposed algorithm does not need to introduce new variables and constraints. Therefore, the proposed algorithm is more suitable for application in engineering.