caa a22 4500 463169301 CHVBK 20180406164808.0 cr unu---uuuuu 170326e20070801xx s 000 0 eng 10.1007/s10957-007-9221-1 doi (NATIONALLICENCE)springer-10.1007/s10957-007-9221-1 Lagrangian Duality and Cone Convexlike Functions [Elektronische Daten] [J. Frenk, G. Kassay] In this paper, we consider first the most important classes of cone convexlike vector-valued functions and give a dual characterization for some of these classes. It turns out that these characterizations are strongly related to the closely convexlike and Ky Fan convex bifunctions occurring within minimax problems. Applying the Lagrangian perturbation approach, we show that some of these classes of cone convexlike vector-valued functions show up naturally in verifying strong Lagrangian duality for finite-dimensional optimization problems. This is achieved by extending classical convexity results for biconjugate functions to the class of so-called almost convex functions. In particular, for a general class of finite-dimensional optimization problems, strong Lagrangian duality holds if some vector-valued function related to this optimization problem is closely K-convexlike and satisfies some additional regularity assumptions. For K a full-dimensional convex cone, it turns out that the conditions for strong Lagrangian duality simplify. Finally, we compare the results obtained by the Lagrangian perturbation approach worked out in this paper with the results achieved by the so-called image space approach initiated by Giannessi. Springer Science+Business Media, LLC, 2007 Cone convexlike functions nationallicence Lagrangian duality nationallicence Frenk J. Econometric Institute, Erasmus University Rotterdam, Rotterdam, Netherlands aut Kassay G. Faculty of Mathematics and Computer Science, Babes-Bolyai University, Cluj, Romania aut Journal of Optimization Theory and Applications Springer US; http://www.springer-ny.com 134/2(2007-08-01), 207-222 0022-3239 134:2<207 2007 134 10957 https://doi.org/10.1007/s10957-007-9221-1 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10957-007-9221-1 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Frenk J. Econometric Institute, Erasmus University Rotterdam, Rotterdam, Netherlands aut NATIONALLICENCE 700 1- Kassay G. Faculty of Mathematics and Computer Science, Babes-Bolyai University, Cluj, Romania aut NATIONALLICENCE 773 0- Journal of Optimization Theory and Applications Springer US; http://www.springer-ny.com 134/2(2007-08-01), 207-222 0022-3239 134:2<207 2007 134 10957 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer