Generalized Fenchel's conjugation formulas and duality for abstract convex functions

Title: Generalized Fenchel's conjugation formulas and duality for abstract convex functions
Creator: Jeyakumar, Vaithilingam; Rubinov, Alex; Wu, Zhiyou
Date: 2007
Type: Text; Journal article
Identifier: http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/43910
Identifier: vital:444
Identifier: ISSN:0022-3239
Abstract: In this paper, we present a generalization of Fenchel's conjugation and derive infimal convolution formulas, duality and subdifferential (and epsilon-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.; C1
Publisher: Springer New York LLC
Relation: Journal of Optimization Theory and Applications Vol. 132, no. 3 (Mar 2007), p. 441-458
Rights: Copyright Springer
Rights: This metadata is freely available under a CCO license
Subject: 0103 Numerical and Computational Mathematics; Global nonaffine supports; Abstract convexity of sets and functions; Generalized Fenchel's duality; Infimal convolutions
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