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A new necessary and sufficient global optimality condition for canonical DC problems

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  • Qinghua Zhang

Abstract

The paper proposes a new necessary and sufficient global optimality condition for canonical DC optimization problems. We analyze the rationale behind Tuy’s standard global optimality condition for canonical DC problems, which relies on the so-called regularity condition and thus can not deal with the widely existing non-regular instances. Then we show how to modify and generalize the standard condition to a new one that does not need regularity assumption, and prove that this new condition is equivalent to other known global optimality conditions. Finally, we show that the cutting plane method, when associated with the new optimality condition, could solve the non-regular canonical DC problems, which significantly enlarges the application of existing cutting plane (outer approximation) algorithms. Copyright Springer Science+Business Media, LLC. 2013

Suggested Citation

  • Qinghua Zhang, 2013. "A new necessary and sufficient global optimality condition for canonical DC problems," Journal of Global Optimization, Springer, vol. 55(3), pages 559-577, March.
    • Handle: RePEc:spr:jglopt:v:55:y:2013:i:3:p:559-577
    DOI: 10.1007/s10898-012-9908-1
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    References listed on IDEAS

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    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. Moustapha Diaby, 1993. "Implicit Enumeration for the Pure Integer 0/1 Minimax Programming Problem," Operations Research, INFORMS, vol. 41(6), pages 1172-1176, December.
    3. H. Tuy, 2003. "On Global Optimality Conditions and Cutting Plane Algorithms," Journal of Optimization Theory and Applications, Springer, vol. 118(1), pages 201-216, July.
    4. 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.
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    Cited by:

    1. M. V. Dolgopolik, 2020. "New global optimality conditions for nonsmooth DC optimization problems," Journal of Global Optimization, Springer, vol. 76(1), pages 25-55, January.
    2. M. V. Dolgopolik, 2022. "DC Semidefinite programming and cone constrained DC optimization I: theory," Computational Optimization and Applications, Springer, vol. 82(3), pages 649-671, July.

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