An approach to fractional programming via D.C. constraints problem: Local search

Abstract

We consider the problem of optimizing the sum of several rational functions via reduction to a problem with d.c. constraints.We propose a method of finding a local solution to the fractional program which can be subsequently used in the global search method based on the global optimality conditions for a problem with nonconvex (d.c.) constraints [21-23]. According to the theory, we construct explicit representations of the constraints in the form of differences of two convex functions and perform a local search method that takes into account the structure of the problem in question. This algorithm was verified on a set of low-dimensional test problems taken from literature as well as on randomly generated problems with up to 200 variables and 200 terms in the sum.