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Global optimization of a rank-two nonconvex program

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  • Riccardo Cambini
  • Claudio Sodini

Abstract

In this paper a solution algorithm for a class of rank-two nonconvex programs having a polyhedral feasible region is proposed. The algorithm is based on the so called optimal level solutions method. Various global optimality conditions are discussed and implemented in order to improve the efficiency of the algorithm. Copyright Springer-Verlag 2010

Suggested Citation

  • 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.
    • Handle: RePEc:spr:mathme:v:71:y:2010:i:1:p:165-180
    DOI: 10.1007/s00186-009-0289-2
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    References listed on IDEAS

    as
    1. Riccardo Cambini & Claudio Sodini, 2002. "A Finite Algorithm for a Particular D.C. Quadratic Programming Problem," Annals of Operations Research, Springer, vol. 117(1), pages 33-49, November.
    2. Alberto Cambini & Laura Martein, 2009. "Generalized Convexity and Optimization," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-540-70876-6, October.
    3. Riccardo Cambini & Claudio Sodini, 2008. "A sequential method for a class of box constrained quadratic programming problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 67(2), pages 223-243, April.
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    Citations

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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. 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.
    4. Riccardo Cambini, 2020. "Underestimation functions for a rank-two partitioning method," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(2), pages 465-489, December.
    5. 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.
    6. 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.

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