Duality in vector optimization:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2009
|
| Series: | Vector optimization
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 385 - 395 |
| Physical Description: | XV, 400 S. 24 cm |
| ISBN: | 9783642028854 |
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MARC
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS 1 INTRODUCTION 1 2 PRELIMINARIES ON CONVEX ANALYSIS AND VECTOR
OPTIMIZATION .. 9 2.1 CONVEX SETS 9 2.1.1 ALGEBRAIC PROPERTIES OF CONVEX
SETS 9 2.1.2 TOPOLOGICAL PROPERTIES OF CONVEX SETS 14 2.2 CONVEX
FUNCTIONS 19 2.2.1 ALGEBRAIC PROPERTIES OF CONVEX FUNCTIONS 19 2.2.2
TOPOLOGICAL PROPERTIES OF CONVEX FUNCTIONS 25 2.3 CONJUGATE FUNCTIONS
AND SUBDIFFERENTIABILITY 30 2.3.1 CONJUGATE FUNCTIONS 30 2.3.2
SUBDIFFERENTIABILITY 38 2.4 MINIMAL AND MAXIMAL ELEMENTS OF SETS 42
2.4.1 MINIMALITY 42 2.4.2 WEAK MINIMALITY 45 2.4.3 PROPER MINIMALITY 46
2.4.4 LINEAR SCALARIZATION 54 2.5 VECTOR OPTIMIZATION PROBLEMS 57 3
CONJUGATE DUALITY IN SCALAR OPTIMIZATION 63 3.1 PERTURBATION THEORY AND
DUAL PROBLEMS 63 3.1.1 THE GENERAL SCALAR OPTIMIZATION PROBLEM 63 3.1.2
OPTIMIZATION PROBLEMS HAVING THE COMPOSITION WITH A LINEAR CONTINUOUS
MAPPING IN THE OBJECTIVE FUNCTION.... 66 3.1.3 OPTIMIZATION PROBLEMS
WITH GEOMETRIC AND CONE CONSTRAINTS 68 3.2 REGULARITY CONDITIONS AND
STRONG DUALITY 73 3.2.1 REGULARITY CONDITIONS FOR THE GENERAL SCALAR
OPTIMIZATION PROBLEM 73 BIBLIOGRAFISCHE INFORMATIONEN
HTTP://D-NB.INFO/994680317 DIGITALISIERT DURCH CONTENTS 3.2.2 REGULARITY
CONDITIONS FOR PROBLEMS HAVING THE COMPOSITION WITH A LINEAR CONTINUOUS
MAPPING IN THE OBJECTIVE FUNCTION 76 3.2.3 REGULARITY CONDITIONS FOR
PROBLEMS WITH GEOMETRIC AND CONE CONSTRAINTS 80 3.3 OPTIMALITY
CONDITIONS AND SADDLE POINTS 86 3.3.1 THE GENERAL SCALAR OPTIMIZATION
PROBLEM 86 3.3.2 PROBLEMS HAVING THE COMPOSITION WITH A LINEAR
CONTINUOUS MAPPING IN THE OBJECTIVE FUNCTION 89 3.3.3 PROBLEMS WITH
GEOMETRIC AND CONE CONSTRAINTS 95 3.4 THE COMPOSED CONVEX OPTIMIZATION
PROBLEM 100 3.4.1 A FIRST DUAL PROBLEM TO (P C ) 100 3.4.2 A SECOND
DUAL PROBLEM TO (P 00 ) 105 3.5 STABLE STRONG DUALITY AND FORMULAE FOR
CONJUGATE FUNCTIONS AND SUBDIFFERENTIALS 109 3.5.1 STABLE STRONG DUALITY
FOR THE GENERAL SCALAR OPTIMIZATION PROBLEM 110 3.5.2 THE COMPOSED
CONVEX OPTIMIZATION PROBLEM ILL 3.5.3 PROBLEMS HAVING THE COMPOSITION
WITH A LINEAR CONTINUOUS MAPPING IN THE OBJECTIVE FUNCTION 114 3.5.4
PROBLEMS WITH GEOMETRIC AND CONE CONSTRAINTS 117 CONJUGATE VECTOR
DUALITY VIA SCALARIZATION 123 4.1 FENCHEL TYPE VECTOR DUALITY 123 4.1.1
DUALITY WITH RESPECT TO PROPERLY EFFICIENT SOLUTIONS 123 4.1.2 DUALITY
WITH RESPECT TO WEAKLY EFFICIENT SOLUTIONS 130 4.2 CONSTRAINED VECTOR
OPTIMIZATION: A GEOMETRIC APPROACH 132 4.2. CONTENTS XI 4.5.1 THE DUALS
INTRODUCED VIA LINEAR SCALARIZATION 173 4.5.2 LINEAR VECTOR DUALITY WITH
RESPECT TO WEAKLY EFFICIENT SOLUTIONS 176 4.5.3 NAKAYAMA S GEOMETRIC
DUAL IN THE LINEAR CASE 178 5 CONJUGATE DUALITY FOR VECTOR OPTIMIZATION
PROBLEMS WITH FINITE DIMENSIONAL IMAGE SPACES 181 5.1 ANOTHER FENCHEL
TYPE VECTOR DUAL PROBLEM 181 5.1.1 DUALITY WITH RESPECT TO PROPERLY
EFFICIENT SOLUTIONS 182 5.1.2 COMPARISONS TO (DV A ) AND {DV$ K ) 192
5.1.3 DUALITY WITH RESPECT TO WEAKLY EFFICIENT SOLUTIONS 194 5.2 A
FAMILY OF FENCHEL-LAGRANGE TYPE VECTOR DUALS 198 5.2.1 DUALITY WITH
RESPECT TO PROPERLY EFFICIENT SOLUTIONS 199 5.2.2 DUALITY WITH RESPECT
TO WEAKLY EFFICIENT SOLUTIONS 209 5.2.3 DUALITY FOR LINEARLY CONSTRAINED
VECTOR OPTIMIZATION PROBLEMS 212 5.3 COMPARISONS BETWEEN DIFFERENT DUALS
TO (PVF C ) 218 5.4 LINEAR VECTOR DUALITY FOR PROBLEMS WITH FINITE
DIMENSIONAL IMAGE SPACES 227 5.4.1 DUALITY WITH RESPECT TO PROPERLY
EFFICIENT SOLUTIONS 227 5.4.2 DUALITY WITH RESPECT TO WEAKLY EFFICIENT
SOLUTIONS 232 5.5 CLASSICAL LINEAR VECTOR DUALITY IN FINITE DIMENSIONAL
SPACES .... 235 5.5.1 DUALITY WITH RESPECT TO EFFICIENT SOLUTIONS 235
5.5.2 DUALITY WITH RESPECT TO WEAKLY EFFICIENT SOLUTIONS 244 6 XII
CONTENTS 6.4 WOLFE AND MOND-WEIR FRACTIONAL DUALITY 290 6.4.1 WOLFE AND
MOND-WEIR DUALITY IN SCALAR FRACTIONAL PROGRAMMING 290 6.4.2 WOLFE AND
MOND-WEIR DUALITY IN VECTOR FRACTIONAL PROGRAMMING 294 6.5 GENERALIZED
WOLFE AND MOND-WEIR DUALITY: A PERTURBATION APPROACH 302 6.5.1 WOLFE
TYPE AND MOND-WEIR TYPE DUALS FOR GENERAL SCALAR OPTIMIZATION PROBLEMS
302 6.5.2 WOLFE TYPE AND MOND-WEIR TYPE DUALS FOR DIFFERENT SCALAR
OPTIMIZATION PROBLEMS 303 6.5.3 WOLFE TYPE AND MOND-WEIR TYPE DUALS FOR
GENERAL VECTOR OPTIMIZATION PROBLEMS 306 7 DUALITY FOR SET-VALUED
OPTIMIZATION PROBLEMS BASED ON VECTOR CONJUGACY 311 7.1 CONJUGATE
DUALITY BASED ON EFFICIENT SOLUTIONS 311 7.1.1 CONJUGATE MAPS AND THE
SUBDIFFERENTIAL OF SET-VALUED MAPS 311 7.1.2 THE PERTURBATION APPROACH
FOR CONJUGATE DUALITY 319 7.1.3 A SPECIAL APPROACH - VECTOR FE-CONJUGACY
AND DUALITY ... 330 7.2 THE SET-VALUED OPTIMIZATION PROBLEM WITH
CONSTRAINTS 334 7.2.1 DUALITY BASED ON GENERAL VECTOR CONJUGACY 335
7.2.2 DUALITY BASED ON VECTOR FC-CONJUGACY 342 7.2.3 STABILITY CRITERIA
346 7.3 THE SET-VALUED OPTIMIZATION PROBLEM HAVING THE COMPOSITION WITH
A LINEAR CONTINUOUS MAPPING IN THE OBJECTIVE FUNCTION.... 352 7.3.1
FENCHEL SET-VALUED DUALITY 352 7.3.2 SET-VALUED GAP MAPS FOR VECTOR
VARIATIONAL INEQUALITIES . 356 7.4 CONJUGATE DUALITY BASED ON WEAKLY
EFFICIENT SOLUTIONS 360 7.4.
|
| any_adam_object | 1 |
| author | Boţ, Radu Ioan 1976- Grad, Sorin-Mihai 1979- Wanka, Gert 1951- |
| author_GND | (DE-588)125003935 (DE-588)129631469 (DE-588)109947576 |
| author_facet | Boţ, Radu Ioan 1976- Grad, Sorin-Mihai 1979- Wanka, Gert 1951- |
| author_role | aut aut aut |
| author_sort | Boţ, Radu Ioan 1976- |
| author_variant | r i b ri rib s m g smg g w gw |
| building | Verbundindex |
| bvnumber | BV035794893 |
| classification_rvk | SK 870 |
| ctrlnum | (OCoLC)439751626 (DE-599)DNB994680317 |
| dewey-full | 519.7 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.7 |
| dewey-search | 519.7 |
| dewey-sort | 3519.7 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:04:44Z |
| institution | BVB |
| isbn | 9783642028854 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018654141 |
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| owner | DE-824 DE-11 DE-29T |
| owner_facet | DE-824 DE-11 DE-29T |
| physical | XV, 400 S. 24 cm |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Springer |
| record_format | marc |
| series2 | Vector optimization |
| spelling | Boţ, Radu Ioan 1976- Verfasser (DE-588)125003935 aut Duality in vector optimization Radu Ioan Boţ ; Sorin-Mihai Grad ; Gert Wanka Berlin [u.a.] Springer 2009 XV, 400 S. 24 cm txt rdacontent n rdamedia nc rdacarrier Vector optimization Literaturverz. S. 385 - 395 Mehrkriterielle Optimierung (DE-588)4610682-0 gnd rswk-swf Dualität (DE-588)4013161-0 gnd rswk-swf Mehrkriterielle Optimierung (DE-588)4610682-0 s Dualität (DE-588)4013161-0 s DE-604 Grad, Sorin-Mihai 1979- Verfasser (DE-588)129631469 aut Wanka, Gert 1951- Verfasser (DE-588)109947576 aut Erscheint auch als Online-Ausgabe 978-3-642-02886-1 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018654141&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Boţ, Radu Ioan 1976- Grad, Sorin-Mihai 1979- Wanka, Gert 1951- Duality in vector optimization Mehrkriterielle Optimierung (DE-588)4610682-0 gnd Dualität (DE-588)4013161-0 gnd |
| subject_GND | (DE-588)4610682-0 (DE-588)4013161-0 |
| title | Duality in vector optimization |
| title_auth | Duality in vector optimization |
| title_exact_search | Duality in vector optimization |
| title_full | Duality in vector optimization Radu Ioan Boţ ; Sorin-Mihai Grad ; Gert Wanka |
| title_fullStr | Duality in vector optimization Radu Ioan Boţ ; Sorin-Mihai Grad ; Gert Wanka |
| title_full_unstemmed | Duality in vector optimization Radu Ioan Boţ ; Sorin-Mihai Grad ; Gert Wanka |
| title_short | Duality in vector optimization |
| title_sort | duality in vector optimization |
| topic | Mehrkriterielle Optimierung (DE-588)4610682-0 gnd Dualität (DE-588)4013161-0 gnd |
| topic_facet | Mehrkriterielle Optimierung Dualität |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018654141&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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