 Geometric conditions for Kuhn-Tucker sufficiency of global optimality in mathematical programmingV. Jeyakumar and S. Srisatkunarajah European Journal of Operational Research, 2009, vol. 194, issue 2, 363-367 Abstract: We present geometric criteria for a feasible point that satisfies the Kuhn-Tucker conditions to be a global minimizer of mathematical programming problems with or without bounds on the variables. The criteria apply to multi-extremal programming problems which may have several local minimizers that are not global. We establish such criteria in terms of underestimators of the Lagrangian of the problem. The underestimators are required to satisfy certain geometric property such as the convexity (or a generalized convexity) property. We show that the biconjugate of the Lagrangian can be chosen as a convex underestimator whenever the biconjugate coincides with the Lagrangian at a point. We also show how suitable underestimators can be constructed for the Lagrangian in the case where the problem has bounds on the variables. Examples are given to illustrate our results. Keywords: Mathematical; programming; problems; Sufficient; optimality; conditions; Multi-extremal; problems; Bounds; on; the; variables; Generalized; convexity; Underestimators (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:194:y:2009:i:2:p:363-367 Access Statistics for this article European Journal of Operational Research is currently edited by Roman Slowinski, Jesus Artalejo, Jean-Charles. Billaut, Robert Dyson and Lorenzo Peccati More articles in European Journal of Operational Research from Elsevier |
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