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On Global Optimality Conditions and Cutting Plane Algorithms

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  • H. Tuy

    (Institute of Mathematics)

Abstract

We discuss global optimality conditions and cutting plane algorithms for DC optimization. The discussion is motivated by certain incorrect results that have appeared recently in the literature on these topics. Incidentally, we investigate the relation of the Tikhonov reciprocity theorem to the optimality conditions for general nonconvex global optimization problems and show how the outer-approximation scheme developed earlier for DC programming can be used to solve a wider class of problems.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:118:y:2003:i:1:d:10.1023_a:1024751811328
    DOI: 10.1023/A:1024751811328
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    References listed on IDEAS

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    1. R. Horst & N. V. Thoai, 1999. "DC Programming: Overview," Journal of Optimization Theory and Applications, Springer, vol. 103(1), pages 1-43, October.
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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.
    3. 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.

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