A Combined Algorithm for Fractional Programming

Jianming Shi ()

Annals of Operations Research, 2001, vol. 103, issue 1, 135-147

Abstract: In this paper, we present an outer approximation algorithm for solving the following problem: max x∈S {f(x)/g(x)}, where f(x)≥0 and g(x)>0 are d.c. (difference of convex) functions over a convex compact subset S of R n . Let π(λ)=max x∈S (f(x)−λg(x)), then the problem is equivalent to finding out a solution of the equation π(λ)=0. Though the monotonicity of π(λ) is well known, it is very time-consuming to solve the previous equation, because that maximizing (f(x)−λg(x)) is very hard due to that maximizing a convex function over a convex set is NP-hard. To avoid such tactics, we give a transformation under which both the objective and the feasible region turn to be d.c. After discussing some properties, we propose a global optimization approach to find an optimal solution for the encountered problem. Copyright Kluwer Academic Publishers 2001

Keywords: fractional programming; cutting plane; global optimization (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1023/A:1012998904482

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