Generalized Fenchel’s Conjugation Formulas and Duality for Abstract Convex Functions

V. Jeyakumar (), A. M. Rubinov () and Z. Y. Wu ()
Additional contact information
V. Jeyakumar: University of New South Wales
A. M. Rubinov: University of Ballarat
Z. Y. Wu: Chongqing Normal University

Journal of Optimization Theory and Applications, 2007, vol. 132, issue 3, No 6, 458 pages

Abstract: Abstract In this paper, we present a generalization of Fenchel’s conjugation and derive infimal convolution formulas, duality and subdifferential (and ε-subdifferential) sum formulas for abstract convex functions. The class of abstract convex functions covers very broad classes of nonconvex functions. A nonaffine global support function technique and an extended sum-epiconjugate technique of convex functions play a crucial role in deriving the results for abstract convex functions. An additivity condition involving global support sets serves as a constraint qualification for the duality.

Keywords: Global nonaffine supports; Abstract convexity of sets and functions; Generalized Fenchel’s duality; Infimal convolutions (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (6)

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DOI: 10.1007/s10957-007-9185-1

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