On solving the sum-of-ratios problem

Tatiana V. Gruzdeva and Alexander S. Strekalovsky

Applied Mathematics and Computation, 2018, vol. 318, issue C, 260-269

Abstract: This paper addresses the development of efficient global search methods for fractional programming problems. Such problems are, in general, nonconvex (with numerous local extremums) and belong to a class of global optimization problems. First, we reduce a rather general fractional programming problem with d.c. functions to solving an equation with a vector parameter that satisfies some nonnegativity assumption. This theorem allows the justified use of the generalized Dinkelbach’s approach for solving fractional programming problems with a d.c. goal function. Based on solving of some d.c. minimization problem, we developed a global search algorithm for fractional programming problems, which was tested on a set of low-dimensional test problems taken from the literature as well as on randomly generated problems with up to 200 variables or 200 terms in the sum.

Keywords: Fractional optimization; Nonconvex optimization; Difference of convex functions; Equation with vector parameter; Global search algorithm (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:318:y:2018:i:c:p:260-269

DOI: 10.1016/j.amc.2017.07.074

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