Maximizing for the sum of ratios of two convex functions over a convex set |
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Authors: | Peiping Shen Weimin LiXiaodi Bai |
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Affiliation: | College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, PR China |
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Abstract: | This paper presents an algorithm for globally maximizing a sum of convex–convex ratios problem with a convex feasible region, which does not require involving all the functions to be differentiable and requires that their sub-gradients can be calculated efficiently. To our knowledge, little progress has been made for globally solving this problem so far. The algorithm uses a branch and bound scheme in which the main computational effort involves solving a sequence of linear programming subproblems. Because of these properties, the algorithm offers a potentially attractive means for globally solving the sum of convex–convex ratios problem over a convex feasible region. It has been proved that the algorithm possesses global convergence. Finally, the numerical experiments are given to show the feasibility of the proposed algorithm. |
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Keywords: | Fractional programming Global optimization Sum of ratios Branch and bound |
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