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Global optimization for the generalized polynomial sum of ratios problem

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Abstract

In this paper, a new deterministic global optimization algorithm is proposed for solving a fractional programming problem whose objective and constraint functions are all defined as the sum of generalized polynomial ratios, which arises in various practical problems. Due to its intrinsic difficulty, less work has been devoted to globally solving this problem. The proposed algorithm is based on reformulating the problem as a monotonic optimization problem, and it turns out that the optimal solution which is provided by the algorithm is adequately guaranteed to be feasible and to be close to the actual optimal solution. Convergence of the algorithm is shown and numerical examples are given to illustrate the feasibility and efficiency of the present algorithm.

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Authors and Affiliations

  1. College of Mathematics and Information Science, Henan Normal University, Xinxiang, 453007, People’s Republic of China

    Peiping Shen, Yuan Ma & Yongqiang Chen

Authors
  1. Peiping Shen
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  2. Yuan Ma
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  3. Yongqiang Chen
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Correspondence to Peiping Shen.

Additional information

Research supported by the Innovation Scientists and Technicians Troop Construction Projects (09410050001) and the Program for Science and Technology Innovation Talents in Universities (2008 HASTIT023) of Henan Province.

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Shen, P., Ma, Y. & Chen, Y. Global optimization for the generalized polynomial sum of ratios problem. J Glob Optim 50, 439–455 (2011). https://doi.org/10.1007/s10898-010-9593-x

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  • DOI: https://doi.org/10.1007/s10898-010-9593-x

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