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Beyond Canonical DC-Optimization: The Single Reverse Polar Problem

Author

Listed:
  • Giancarlo Bigi

    (Università di Pisa)

  • Antonio Frangioni

    (Università di Pisa)

  • Qinghua Zhang

    (Wuhan University)

Abstract

We propose a novel generalization of the Canonical Difference of Convex problem (CDC), and we study the convergence of outer approximation algorithms for its solution, which use an approximated oracle for checking the global optimality conditions. Although the approximated optimality conditions are similar to those of CDC, this new class of problems is shown to significantly differ from its special case. Indeed, outer approximation approaches for CDC need be substantially modified in order to cope with the more general problem, bringing to new algorithms. We develop a hierarchy of conditions that guarantee global convergence, and we build three different cutting plane algorithms relying on them.

Suggested Citation

  • Giancarlo Bigi & Antonio Frangioni & Qinghua Zhang, 2012. "Beyond Canonical DC-Optimization: The Single Reverse Polar Problem," Journal of Optimization Theory and Applications, Springer, vol. 155(2), pages 430-452, November.
  • Handle: RePEc:spr:joptap:v:155:y:2012:i:2:d:10.1007_s10957-012-0069-7
    DOI: 10.1007/s10957-012-0069-7
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    References listed on IDEAS

    as
    1. Fulop, Janos, 1990. "A finite cutting plane method for solving linear programs with an additional reverse convex constraint," European Journal of Operational Research, Elsevier, vol. 44(3), pages 395-409, February.
    2. Rafael Blanquero & Emilio Carrizosa & Pierre Hansen, 2009. "Locating Objects in the Plane Using Global Optimization Techniques," Mathematics of Operations Research, INFORMS, vol. 34(4), pages 837-858, November.
    3. Giancarlo Bigi & Antonio Frangioni & Qinghua Zhang, 2010. "Outer approximation algorithms for canonical DC problems," Journal of Global Optimization, Springer, vol. 46(2), pages 163-189, February.
    Full references (including those not matched with items on IDEAS)

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