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Global optimization for the sum of generalized polynomial fractional functions

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  • Shen Pei-Ping
  • Yuan Gui-Xia

Abstract

In this paper, a branch and bound approach is proposed for global optimization problem (P) of the sum of generalized polynomial fractional functions under generalized polynomial constraints, which arises in various practical problems. Due to its intrinsic difficulty, less work has been devoted to globally solving this problem. By utilizing an equivalent problem and some linear underestimating approximations, a linear relaxation programming problem of the equivalent form is obtained. Consequently, the initial non-convex nonlinear problem (P) is reduced to a sequence of linear programming problems through successively refining the feasible region of linear relaxation problem. The proposed algorithm is convergent to the global minimum of the primal problem by means of the solutions to a series of linear programming problems. Numerical results show that the proposed algorithm is feasible and can successfully be used to solve the present problem (P). Copyright Springer-Verlag 2007

Suggested Citation

  • Shen Pei-Ping & Yuan Gui-Xia, 2007. "Global optimization for the sum of generalized polynomial fractional functions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 65(3), pages 445-459, June.
    • Handle: RePEc:spr:mathme:v:65:y:2007:i:3:p:445-459
    DOI: 10.1007/s00186-006-0130-0
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    Cited by:

    1. Tajbakhsh, Alireza & Hassini, Elkafi, 2018. "Evaluating sustainability performance in fossil-fuel power plants using a two-stage data envelopment analysis," Energy Economics, Elsevier, vol. 74(C), pages 154-178.
    2. Peiping Shen & Yuan Ma & Yongqiang Chen, 2011. "Global optimization for the generalized polynomial sum of ratios problem," Journal of Global Optimization, Springer, vol. 50(3), pages 439-455, July.
    3. Vandana Goyal & Namrata Rani & Deepak Gupta, 2022. "FGP approach to quadratically constrained multi-objective quadratic fractional programming with parametric functions," OPSEARCH, Springer;Operational Research Society of India, vol. 59(2), pages 594-602, June.

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