Conical Partition Algorithm for Maximizing the Sum of dc Ratios |
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| Authors: | Yang?Dai Email author" target="_blank">Jianming?ShiEmail author Shouyang?Wang |
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| Institution: | (1) Department of Bioengineering (MC063), The University of Illinois at Chicago, 851 S. Morgan Street, Chicago, 60607-7052, IL, USA;(2) Department of Computer Science and Systems Engineering, Muroran Institute of Technology, 27-1 Mizumoto-cho, Muroran 050-8585, Japan;(3) Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Zhongguancun, Beijing, 100080, China |
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| Abstract: | The following problem is considered in this paper:
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.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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| Keywords: | cutting plane fractional programming global optimization outer approximation sum of ratios |
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