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A parametric solution algorithm for a class of rank-two nonconvex programs

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Listed:
  • Riccardo Cambini
  • Claudio Sodini

Abstract

The aim of this paper is to propose a solution algorithm for a particular class of rank-two nonconvex programs having a polyhedral feasible region. The algorithm lies within the class of the so called “optimal level solutions” parametric methods. The subproblems obtained by means of this parametrical approach are quadratic convex ones, but not necessarily neither strictly convex nor linear. For this very reason, in order to solve in an unifying framework all of the considered rank-two nonconvex programs a new approach needs to be proposed. The efficiency of the algorithm is improved by means of the use of underestimation functions. The results of a computational test are provided and discussed. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:60:y:2014:i:4:p:649-662
    DOI: 10.1007/s10898-013-0115-5
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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. 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.
    3. Alberto Cambini & Laura Martein, 2009. "Generalized Convexity and Optimization," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-540-70876-6, December.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Nonconvex programs; Low-rank programs; Quadratic programs; Global optimization; C61; C63;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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