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On saddle points in nonconvex semi-infinite programming

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  • Francisco Guerra-Vázquez
  • Jan-J. Rückmann
  • Ralf Werner

Abstract

In this paper we apply two convexification procedures to the Lagrangian of a nonconvex semi-infinite programming problem. Under the reduction approach it is shown that, locally around a local minimizer, this problem can be transformed equivalently in such a way that the transformed Lagrangian fulfills saddle point optimality conditions, where for the first procedure both the original objective function and constraints (and for the second procedure only the constraints) are substituted by their pth powers with sufficiently large power p. These results allow that local duality theory and corresponding numerical methods (e.g. dual search) can be applied to a broader class of nonconvex problems. Copyright Springer Science+Business Media, LLC. 2012

Suggested Citation

  • Francisco Guerra-Vázquez & Jan-J. Rückmann & Ralf Werner, 2012. "On saddle points in nonconvex semi-infinite programming," Journal of Global Optimization, Springer, vol. 54(3), pages 433-447, November.
    • Handle: RePEc:spr:jglopt:v:54:y:2012:i:3:p:433-447
    DOI: 10.1007/s10898-011-9753-7
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    References listed on IDEAS

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    1. Qingxiang Zhang, 2009. "Optimality conditions and duality for semi-infinite programming involving B-arcwise connected functions," Computational Optimization and Applications, Springer, vol. 45(4), pages 615-629, December.
    2. Z. K. Xu, 1997. "Local Saddle Points and Convexification for Nonconvex Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 94(3), pages 739-746, September.
    3. Nader Kanzi, 2011. "Necessary optimality conditions for nonsmooth semi-infinite programming problems," Journal of Global Optimization, Springer, vol. 49(4), pages 713-725, April.
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    Cited by:

    1. Hong Yang & Angang Cui, 2023. "The Sufficiency of Solutions for Non-smooth Minimax Fractional Semi-Infinite Programming with ( B K ,ρ )−Invexity," Mathematics, MDPI, vol. 11(20), pages 1-13, October.

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