CONTENTSIntroduction...........................................................................................................51. Preliminaries on convex and set-valued analysis..............................................6 1.1. Convexity of sets...........................................................................................6 1.2. Convexity of set-valued mappings.................................................................9 1.3. Closed convex processes and invex set-valued mappings..........................122. Vector optimization problems...........................................................................14 2.1. Characterization for optimal points of a set..................................................14 2.2. Characterization for optimal solutions of an optimization problem................173. Lagrangian multiplier rule................................................................................19 3.1. Lagrangian conditions for weak optimality...................................................19 3.2. Lagrangian conditions for optimality.............................................................21 3.3. Lagrangian conditions for invex set-valued mappings.................................284. Lagrangian duality...........................................................................................33 4.1. Duality for weak optimality............................................................................34 4.2. Duality for optimality.....................................................................................35 4.3. Duality for invex set-valued mappings..........................................................365. Geometric duality.............................................................................................37 5.1. A general duality principle for sets...............................................................37 5.2. A geometric approach to duality...................................................................39 5.3. Linear optimization problems.......................................................................426. Conjugate duality.............................................................................................45 6.1. Conjugate mappings and subdifferentials....................................................45 6.2. A general conjugate duality..........................................................................50 6.3. Duality in vector optimization with constraints...............................................55 6.4. The Fenchel type duality..............................................................................59References...........................................................................................................62List of symbols......................................................................................................67Index.....................................................................................................................68
1991 Mathematics Subject Classification: 90C29, 90C26, 90C30.
@book{bwmeta1.element.zamlynska-acac4a76-3c12-4086-b233-4b0d90e5ce8f,
author = {Song Wen},
title = {Duality in set-valued optimization},
series = {GDML\_Books},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
address = {Warszawa},
year = {1998},
zbl = {0934.90070},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.zamlynska-acac4a76-3c12-4086-b233-4b0d90e5ce8f}
}
Song Wen. Duality in set-valued optimization. GDML_Books (1998), http://gdmltest.u-ga.fr/item/bwmeta1.element.zamlynska-acac4a76-3c12-4086-b233-4b0d90e5ce8f/