Lagrangian Duality and Cone Convexlike Functions
21 Pages Posted: 8 Sep 2005
Date Written: April 3, 2005
In this paper we will show that the closely K-convexlike vector-valued functions with K Rm a nonempty convex cone and related classes of vector-valued functions discussed in the literature arise naturally within the theory of biconjugate functions applied to the Lagrangian perturbation scheme in finite dimensional optimization. For these classes of vector-valued functions an equivalent characterization of the dual objective function associated with the Lagrangian is derived by means of a dual representation of the relative interior of a convex cone. It turns out that these characterizations are strongly related to the closely convexlike and Ky-Fan convex bifunctions occurring within minimax problems. Also it is shown for a general class of finite dimensional optimization problems that strong Lagrangian duality holds in case a vector-valued function related to the functions in this optimization problem is closely K-convexlike and satisfies some additional regularity condition.
Keywords: Lagrangian duality
JEL Classification: M, M11, C69, R4
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