A new look at fractional programming
Journal of Optimization Theory and Applications
Generalized linear multiplicative and fractional programming
Annals of Operations Research
Optimizing the sum of linear fractional functions
Recent advances in global optimization
Optimizing the sum of linear fractional functions and applications
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Solving the Sum-of-Ratios Problem by an Interior-Point Method
Journal of Global Optimization
A branch-and-bound algorithm for maximizing the sum of several linear ratios
Journal of Global Optimization
Using concave envelopes to globally solve the nonlinear sum of ratios problem
Journal of Global Optimization
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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.