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Generating the efficient frontier of a class of bicriteria generalized fractional programming

Author

Listed:
  • Riccardo Cambini

    (University of Pisa)

  • Laura Carosi

    (University of Pisa)

  • Laura Martein

    (University of Pisa)

Abstract

In this paper, a particular class of bicriteria maximization problems over a compact polyhedron is considered. The first component of the objective function is the ratio of powers of affine functions and the second one is linear. Several theoretical properties are provided, such as the pseudoconcavity of the first criterium of the objective function, the connectedness and compactness of both the efficient frontier and the set of efficient points. The obtained results allow us to propose a new simplex-like solution method for generating the whole efficient frontier; to better clarify the use of the suggested algorithm, several examples are described and the results of a computational test are presented.

Suggested Citation

  • 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.
  • Handle: RePEc:spr:decfin:v:40:y:2017:i:1:d:10.1007_s10203-017-0196-6
    DOI: 10.1007/s10203-017-0196-6
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    References listed on IDEAS

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    1. Igor V. Konnov & Dinh The Luc & Alexander M. Rubinov, 2006. "Generalized Convexity and Related Topics," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-540-37007-9, October.
    2. 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.
    3. A. Daniilidis & N. Hadjisavvas & S. Schaible, 1997. "Connectedness of the Efficient Set for Three-Objective Quasiconcave Maximization Problems," Journal of Optimization Theory and Applications, Springer, vol. 93(3), pages 517-524, June.
    4. Laura Martein & Valerio Bertolucci, 2007. "A Sequential Method for a Class of Bicriteria Problems," Lecture Notes in Economics and Mathematical Systems, in: Generalized Convexity and Related Topics, pages 347-358, Springer.
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    Cited by:

    1. 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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    More about this item

    Keywords

    Bicriteria programming; Generalized fractional programming; Pseudoconcavity;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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