Lagrangian Duality and Cone Convexlike Functions

21 Pages Posted: 8 Sep 2005

See all articles by J. B. G. Frenk

J. B. G. Frenk

Erasmus University, Rotterdam (EUR) - Department of Econometrics ; Erasmus University, Rotterdam (EUR) - Erasmus Research Institute of Management (ERIM)

G. Kassay

Babes-Bolyai University - Faculty of Mathematics and Computer Science

Date Written: April 3, 2005

Abstract

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

Suggested Citation

Frenk, J.B.G. (Hans) and Kassay, G., Lagrangian Duality and Cone Convexlike Functions (April 3, 2005). Erasmus Research Institute of Management (ERIM), Erasmus University Rotterdam, Research Paper Series, Forthcoming, Available at SSRN: https://ssrn.com/abstract=797928

J.B.G. (Hans) Frenk

Erasmus University, Rotterdam (EUR) - Department of Econometrics ( email )

P.O. Box 1738
3000 DR Rotterdam
Netherlands
+31 0 10 408 1257 (Phone)
+31 0 10 408 9162 (Fax)

Erasmus University, Rotterdam (EUR) - Erasmus Research Institute of Management (ERIM)

P.O. Box 1738
3000 DR Rotterdam
Netherlands

G. Kassay (Contact Author)

Babes-Bolyai University - Faculty of Mathematics and Computer Science ( email )

Str. Mihail Kogalniceanu nr. 1
Cluj-Napoca, RO-400,084
Romania

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