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A Characterization of the Lagrange-Karush-Kuhn-Tucker Property

Dominique Azé (dominique.aze***at***math.univ-toulouse.fr)

Abstract: In this note, we revisit the classical first order necessary condition in mathematical programming in infinite dimension. We show that existence of Lagrange-Karush-Kuhn-Tucker multipliers is equivalent to the existence of an error bound for the constraint set, and is also equivalent to a generalized Abadie's qualification condition. These results extend widely previous one like by removing convexity type assumptions on the data.

Keywords: Lagrange and Karush-Kuhn-Tucker multipliers, error bounds, Abadie's qualification condition

Category 1: Nonlinear Optimization

Category 2: Convex and Nonsmooth Optimization

Citation: Institut de Mathématiques de Toulouse, December 2014

Download: [PDF]

Entry Submitted: 12/08/2014
Entry Accepted: 12/08/2014
Entry Last Modified: 12/16/2015

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