Abstract
The following problem is considered in this paper: \(max_{x\in d\{\Sigma^m_{j=1}g_j(x)|h_j(x)\},}\, where\,g_j(x)\geq 0\, and\,h_j(x) > 0, j = 1,\ldots,m,\) are d.c. (difference of convex) functions over a convex compact set D in R^n. Specifically, it is reformulated into the problem of maximizing a linear objective function over a feasible region defined by multiple reverse convex functions. Several favorable properties are developed and a branch-and-bound algorithm based on the conical partition and the outer approximation scheme is presented. Preliminary results of numerical experiments are reported on the efficiency of the proposed algorithm.
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AMS Subject Classifications: 90C32, 90C30, 65K05.
The authors were partially supported by a Grant-in-Aid (Yang Dai: C-13650444; Jianming Shi and Shouyang Wang: C-14550405) of the Ministry of Education, Science, Sports and Culture of Japan.
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Dai, Y., Shi, J. & Wang, S. Conical Partition Algorithm for Maximizing the Sum of dc Ratios. J Glob Optim 31, 253–270 (2005). https://doi.org/10.1007/s10898-004-5699-3
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DOI: https://doi.org/10.1007/s10898-004-5699-3