Duality in set-valued optimization

Song Wen

  • Publisher: Instytut Matematyczny Polskiej Akademi Nauk(Warszawa), 1998

Abstract

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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.....................................................................................................................681991 Mathematics Subject Classification: 90C29, 90C26, 90C30.

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Song Wen. Duality in set-valued optimization. Warszawa: Instytut Matematyczny Polskiej Akademi Nauk, 1998. <http://eudml.org/doc/271246>.

@book{SongWen1998,
abstract = {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.....................................................................................................................681991 Mathematics Subject Classification: 90C29, 90C26, 90C30.},
author = {Song Wen},
keywords = {set valued map; duality; vector optimization; Lagrangean multipliers},
language = {eng},
location = {Warszawa},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
title = {Duality in set-valued optimization},
url = {http://eudml.org/doc/271246},
year = {1998},
}

TY - BOOK
AU - Song Wen
TI - Duality in set-valued optimization
PY - 1998
CY - Warszawa
PB - Instytut Matematyczny Polskiej Akademi Nauk
AB - 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.....................................................................................................................681991 Mathematics Subject Classification: 90C29, 90C26, 90C30.
LA - eng
KW - set valued map; duality; vector optimization; Lagrangean multipliers
UR - http://eudml.org/doc/271246
ER -

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