Journal of Global Optimization

, Volume 50, Issue 3, pp 439–455 | Cite as

Global optimization for the generalized polynomial sum of ratios problem

  • Peiping Shen
  • Yuan Ma
  • Yongqiang Chen


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.


Global optimization Generalized polynomial Fractional programming Sum of ratios Nonisolated optimal solution 


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© Springer Science+Business Media, LLC. 2010

Authors and Affiliations

  1. 1.College of Mathematics and Information ScienceHenan Normal UniversityXinxiangPeople’s Republic of China

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