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A unifying approach to solve some classes of rank-three multiplicative and fractional programs involving linear functions

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  • Cambini, Riccardo
  • Sodini, Claudio

Abstract

The aim of this paper is to propose a solution algorithm for solving a class of low-rank programs involving linear functions and having a polyhedral feasible region. In particular, the proposed solution method solves in an unifying approach some classes of rank-three multiplicative and fractional programs. The algorithm is based on the so called optimal level solutions method. Some optimality conditions are used to improve the performance of the proposed algorithm. Results of a computational test are provided.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:207:y:2010:i:1:p:25-29
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    References listed on IDEAS

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    1. Riccardo Cambini & Claudio Sodini, 2007. "A Unifying Approach to Solve a Class of Parametrically-Convexifiable Problems," Lecture Notes in Economics and Mathematical Systems, in: Generalized Convexity and Related Topics, pages 149-166, Springer.
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    Cited by:

    1. Peiping Shen & Kaimin Wang & Ting Lu, 2020. "Outer space branch and bound algorithm for solving linear multiplicative programming problems," Journal of Global Optimization, Springer, vol. 78(3), pages 453-482, November.
    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. Laura Carosi, 2017. "Pseudoconvexity on a closed convex set: an application to a wide class of generalized fractional functions," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 40(1), pages 145-158, November.
    4. Peiping Shen & Dianxiao Wu & Kaimin Wang, 2023. "Globally minimizing a class of linear multiplicative forms via simplicial branch-and-bound," Journal of Global Optimization, Springer, vol. 86(2), pages 303-321, June.
    5. Riccardo Cambini & Claudio Sodini, 2014. "A parametric solution algorithm for a class of rank-two nonconvex programs," Journal of Global Optimization, Springer, vol. 60(4), pages 649-662, December.
    6. Ashtiani, Alireza M. & Ferreira, Paulo A.V., 2015. "A branch-and-cut algorithm for a class of sum-of-ratios problems," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 596-608.

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