1. Global optimization for sum of generalized fractional functions
- Author
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Peiping Shen and Chun-Feng Wang
- Subjects
Mathematical optimization ,Linear programming ,Linear relaxation ,Applied Mathematics ,Generalized fractional programming ,Nonlinear programming ,Linear-fractional programming ,Computational Mathematics ,Fractional programming ,Linearization ,Global optimization ,Branch and bound ,Criss-cross algorithm ,Geometric programming ,Mathematics - Abstract
This paper considers the solution of generalized fractional programming (GFP) problem which contains various variants such as a sum or product of a finite number of ratios of linear functions, polynomial fractional programming, generalized geometric programming, etc. over a polytope. For such problems, we present an efficient unified method. In this method, by utilizing a transformation and a two-part linearization method, a sequence of linear programming relaxations of the initial nonconvex programming problem are derived which are embedded in a branch-and-bound algorithm. Numerical results are given to show the feasibility and effectiveness of the proposed algorithm.
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