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.
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This work has been supported by the Russian Science Foundation, Project N 15-11-20015.
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Gruzdeva, T., Strekalovsky, A. (2016). An Approach to Fractional Programming via D.C. Constraints Problem: Local Search. In: Kochetov, Y., Khachay, M., Beresnev, V., Nurminski, E., Pardalos, P. (eds) Discrete Optimization and Operations Research. DOOR 2016. Lecture Notes in Computer Science(), vol 9869. Springer, Cham. https://doi.org/10.1007/978-3-319-44914-2_32
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