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New Sufficiency for Global Optimality and Duality of Mathematical Programming Problems via Underestimators

Author

Listed:
  • V. Jeyakumar

    (University of New South Wales)

  • S. Srisatkunarajah

    (University of New South Wales)

Abstract

We present new conditions for a Karush-Kuhn-Tucker point to be a global minimizer of a mathematical programming problem which may have many local minimizers that are not global. The new conditions make use of underestimators of the Lagrangian at the Karush-Kuhn-Tucker point. We establish that a Karush-Kuhn-Tucker point is a global minimizer if the Lagrangian admits an underestimator, which is convex or, more generally, has the property that every stationary point is a global minimizer. In particular, we obtain sufficient conditions by using the fact that the biconjugate function of the Lagrangian is a convex underestimator at a point whenever it coincides with the Lagrangian at that point. We present also sufficient conditions for weak and strong duality results in terms of underestimators.

Suggested Citation

  • V. Jeyakumar & S. Srisatkunarajah, 2009. "New Sufficiency for Global Optimality and Duality of Mathematical Programming Problems via Underestimators," Journal of Optimization Theory and Applications, Springer, vol. 140(2), pages 239-247, February.
    • Handle: RePEc:spr:joptap:v:140:y:2009:i:2:d:10.1007_s10957-008-9438-7
    DOI: 10.1007/s10957-008-9438-7
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    Cited by:

    1. Xue-Gang Zhou & Xiao-Peng Yang & Bing-Yuan Cao, 2015. "Global optimality conditions for cubic minimization problems with cubic constraints," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 82(3), pages 243-264, December.

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