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

V. Jeyakumar () and S. Srisatkunarajah
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V. Jeyakumar: University of New South Wales
S. Srisatkunarajah: University of New South Wales

Journal of Optimization Theory and Applications, 2009, vol. 140, issue 2, No 4, 239-247

Abstract: 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.

Keywords: Karush-Kuhn-Tucker conditions; Sufficient optimality conditions; Strong duality; Underestimators; Biconjugate functions (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-008-9438-7

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