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Duality in set-valued optimization

Autorzy
Seria
Rozprawy Matematyczne tom/nr w serii: 375 wydano: 1998
Zawartość
Warianty tytułu
Abstrakty
EN
CONTENTS
Introduction...........................................................................................................5
1. 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..........................12
2. Vector optimization problems...........................................................................14
 2.1. Characterization for optimal points of a set..................................................14
 2.2. Characterization for optimal solutions of an optimization problem................17
3. 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.................................28
4. Lagrangian duality...........................................................................................33
 4.1. Duality for weak optimality............................................................................34
 4.2. Duality for optimality.....................................................................................35
 4.3. Duality for invex set-valued mappings..........................................................36
5. 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.......................................................................42
6. 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..............................................................................59
References...........................................................................................................62
List of symbols......................................................................................................67
Index.....................................................................................................................68
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne tom/nr w serii: 375
Liczba stron
69
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CCCLXXV
Daty
wydano
1998
otrzymano
1997-11-03
poprawiono
1998-01-15
Twórcy
autor
  • Department of Mathematics, Harbin Normal University, 150080 Harbin, China, song@impan.gov.pl
  • Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-950 Warszawa, Poland
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1991 Mathematics Subject Classification: 90C29, 90C26, 90C30.
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