caa a22 4500 463169972 CHVBK 20180406164810.0 cr unu---uuuuu 170326e20070301xx s 000 0 eng 10.1007/s10957-007-9185-1 doi (NATIONALLICENCE)springer-10.1007/s10957-007-9185-1 Generalized Fenchel's Conjugation Formulas and Duality for Abstract Convex Functions [Elektronische Daten] [V. Jeyakumar, A. Rubinov, Z. Wu] 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. Anonaffine 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. Springer Science+Business Media, LLC, 2007 Global nonaffine supports nationallicence Abstract convexity of sets and functions nationallicence Generalized Fenchel's duality nationallicence Infimal convolutions nationallicence Jeyakumar V. Department of Applied Mathematics, University of New South Wales, Sydney, Australia aut Rubinov A. CIAO, School of Information Technology and Mathematical Sciences, University of Ballarat, Ballarat, Victoria, Australia aut Wu Z. School of Mathematics and Computer Science, Chongqing Normal University, Chongqing, China aut Journal of Optimization Theory and Applications Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 132/3(2007-03-01), 441-458 0022-3239 132:3<441 2007 132 10957 https://doi.org/10.1007/s10957-007-9185-1 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10957-007-9185-1 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Jeyakumar V. Department of Applied Mathematics, University of New South Wales, Sydney, Australia aut NATIONALLICENCE 700 1- Rubinov A. CIAO, School of Information Technology and Mathematical Sciences, University of Ballarat, Ballarat, Victoria, Australia aut NATIONALLICENCE 700 1- Wu Z. School of Mathematics and Computer Science, Chongqing Normal University, Chongqing, China aut NATIONALLICENCE 773 0- Journal of Optimization Theory and Applications Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 132/3(2007-03-01), 441-458 0022-3239 132:3<441 2007 132 10957 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer