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Simplex-like sequential methods for a class of generalized fractional programs

Author

Listed:
  • Riccardo Cambini

    (University of Pisa)

  • Laura Carosi

    (University of Pisa)

  • Laura Martein

    (University of Pisa)

  • Ezat Valipour

    (Shahid Bahonar University of Kerman)

Abstract

A sequential method for a class of generalized fractional programming problems is proposed. The considered objective function is the ratio of powers of affine functions and the feasible region is a polyhedron, not necessarily bounded. Theoretical properties of the optimization problem are first established and the maximal domains of pseudoconcavity are characterized. When the objective function is pseudoconcave in the feasible region, the proposed algorithm takes advantage of the nice optimization properties of pseudoconcave functions; the particular structure of the objective function allows to provide a simplex-like algorithm even when the objective function is not pseudoconcave. Computational results validate the nice performance of the proposed algorithm.

Suggested Citation

  • Riccardo Cambini & Laura Carosi & Laura Martein & Ezat Valipour, 2017. "Simplex-like sequential methods for a class of generalized fractional programs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 85(1), pages 77-96, February.
    • Handle: RePEc:spr:mathme:v:85:y:2017:i:1:d:10.1007_s00186-016-0556-y
    DOI: 10.1007/s00186-016-0556-y
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    References listed on IDEAS

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    1. Cambini, Riccardo & Sodini, Claudio, 2010. "A unifying approach to solve some classes of rank-three multiplicative and fractional programs involving linear functions," European Journal of Operational Research, Elsevier, vol. 207(1), pages 25-29, November.
    2. Laura Carosi & Laura Martein, 2008. "A sequential method for a class of pseudoconcave fractional problems," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 16(2), pages 153-164, June.
    3. Riccardo Cambini & Claudio Sodini, 2010. "Global optimization of a rank-two nonconvex program," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 71(1), pages 165-180, February.
    4. Alberto Cambini & Laura Martein, 2009. "Generalized Convexity and Optimization," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-540-70876-6, December.
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    Cited by:

    1. Riccardo Cambini & Laura Carosi & Laura Martein, 2017. "Generating the efficient frontier of a class of bicriteria generalized fractional programming," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 40(1), pages 81-101, November.
    2. Riccardo Cambini & Giovanna D’Inverno, 2024. "Rank-two programs involving linear fractional functions," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 47(1), pages 299-325, June.

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