Set-valued optimization: an introduction with applications
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| Main Authors: | , , |
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| Format: | Book |
| Language: | English |
| Published: |
Heidelberg ; New York ; Dordrecht ; London
Springer
[2015]
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| Series: | Vector optimization
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| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | xxii, 765 Seiten Diagramme |
| ISBN: | 9783642542640 |
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MARC
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| 100 | 1 | |a Khan, Akhtar A. |e Verfasser |0 (DE-588)1106856139 |4 aut | |
| 245 | 1 | 0 | |a Set-valued optimization |b an introduction with applications |c Akhtar A. Khan, Christiane Tammer, Constantin Zălinescu |
| 264 | 1 | |a Heidelberg ; New York ; Dordrecht ; London |b Springer |c [2015] | |
| 264 | 4 | |c © 2015 | |
| 300 | |a xxii, 765 Seiten |b Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Vector optimization | |
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| 653 | |a Research | ||
| 653 | |a cone properties | ||
| 653 | |a Hahn-Banach extension | ||
| 653 | |a nonconvex separation | ||
| 653 | |a existence theorem | ||
| 653 | |a minimal point | ||
| 653 | |a variational analysis | ||
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| 689 | 0 | 1 | |a Optimierung |0 (DE-588)4043664-0 |D s |
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| 700 | 1 | |a Zălinescu, Constantin |d 1952- |e Verfasser |0 (DE-588)1146393032 |4 aut | |
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Record in the Search Index
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CONTENTS
1 INTRODUCTION 1
1.1 MOTIVATING EXAMPLES 1
1.2 BOOK STRUCTURE 4
1.3 USEFUL NOTATION 9
2 ORDER RELATIONS AND ORDERING CONES 11
2.1 ORDER RELATIONS 11
2.2 CONE PROPERTIES RELATED TO THE TOPOLOGY AND THE ORDER 17
2.3 CONVEXITY NOTIONS FOR SETS AND SET-VALUED MAPS 22
2.4 SOLUTION CONCEPTS IN VECTOR OPTIMIZATION 28
2.5 VECTOR OPTIMIZATION PROBLEMS WITH VARIABLE ORDERING
STRUCTURE 43
2.6 SOLUTION CONCEPTS IN SET-VALUED OPTIMIZATION 45
2.6.1 SOLUTION CONCEPTS BASED ON VECTOR APPROACH 45
2.6.2 SOLUTION CONCEPTS BASED ON SET APPROACH 48
2.6.3 SOLUTION CONCEPTS BASED ON LATTICE STRUCTURE 55
2.6.4 THE EMBEDDING APPROACH BY KUROIWA 65
2.6.5 SOLUTION CONCEPTS WITH RESPECT TO ABSTRACT
PREFERENCE RELATIONS 67
2.6.6 SET-VALUED OPTIMIZATION PROBLEMS
WITH VARIABLE ORDERING STRUCTURE 70
2.6.7 APPROXIMATE SOLUTIONS OF SET-VALUED
OPTIMIZATION PROBLEMS 73
2.7 RELATIONSHIPS BETWEEN SOLUTION CONCEPTS 74
3 CONTINUITY AND DIFFERENTIABILITY 77
3.1 CONTINUITY NOTIONS FOR SET-VALUED MAPS 77
3.2 CONTINUITY PROPERTIES OF SET-VALUED MAPS UNDER
CONVEXITY ASSUMPTIONS 90
3.3 LIPSCHITZ PROPERTIES FOR SINGLE-VALUED AND SET-VALUED MAPS 96
3.4 CLARKE'S NORMAL CONE AND SUBDIFFERENTIAL 102
XIII
HTTP://D-NB.INFO/1046584243
XIV CONTENTS
3.5 LIMITING CONES AND GENERALIZED DIFFERENTIABILITY 103
3.6 APPROXIMATE CONES AND GENERALIZED DIFFERENTIABILITY 107
4 TANGENT CONES AND TANGENT SETS 109
4.1 FIRST-ORDER TANGENT CONES 110
4.1.1 THE RADIAL TANGENT CONE AND THE FEASIBLE
TANGENT CONE 110
4.1.2 THE CONTINGENT CONE AND THE INTERIORLY
CONTINGENT CONE 112
4.1.3 THE ADJACENT CONE AND THE INTERIORLY
ADJACENT CONE 120
4.2 MODIFIED FIRST-ORDER TANGENT CONES 123
4.2.1 THE MODIFIED RADIAL AND THE MODIFIED
FEASIBLE TANGENT CONES 124
4.2.2 THE MODIFIED CONTINGENT AND THE MODIFIED
INTERIORLY CONTINGENT CONES 124
4.2.3 THE MODIFIED ADJACENT AND THE MODIFIED
INTERIORLY ADJACENT CONES 126
4.3 MISCELLANEOUS PROPERTIES OF FIRST-ORDER TANGENT CONES 129
4.4 FIRST-ORDER TANGENT CONES ON CONVEX SETS 132
4.4.1 CONNECTIONS AMONG FIRST-ORDER TANGENT
CONES ON CONVEX SETS 132
4.4.2 PROPERTIES OF FIRST-ORDER TANGENT CONES
ON CONVEX SETS 137
4.5 FIRST-ORDER LOCAL CONE APPROXIMATION 143
4.6 CONVEX SUBCONES OF THE CONTINGENT CONE 147
4.7 FIRST-ORDER INVERSION THEOREMS AND INTERSECTION FORMULAS 156
4.8 EXPRESSIONS OF THE CONTINGENT CONE ON SOME
CONSTRAINT SETS 161
4.9 SECOND-ORDER TANGENT SETS 169
4.9.1 SECOND-ORDER RADIAL TANGENT SET
AND SECOND-ORDER FEASIBLE TANGENT SET 170
4.9.2 SECOND-ORDER CONTINGENT SET
AND SECOND-ORDER INTERIORLY CONTINGENT SET 170
4.9.3 SECOND-ORDER ADJACENT SET AND
SECOND-ORDER INTERIORLY ADJACENT SET 173
4.10 GENERALIZED SECOND-ORDER TANGENT SETS 175
4.11 SECOND-ORDER ASYMPTOTIC TANGENT CONES 181
4.11.1 SECOND-ORDER ASYMPTOTIC FEASIBLE TANGENT
CONE AND SECOND-ORDER ASYMPTOTIC RADIAL
TANGENT CONE 182
4.11.2 SECOND-ORDER ASYMPTOTIC CONTINGENT CONE
AND SECOND-ORDER ASYMPTOTIC INTERIORLY
CONTINGENT CONE 183
CONTENTS XV
4.11.3 SECOND-ORDER ASYMPTOTIC ADJACENT CONE
AND SECOND-ORDER ASYMPTOTIC INTERIORLY
ADJACENT CONE 185
4.12 MISCELLANEOUS PROPERTIES OF SECOND-ORDER TANGENT
SETS AND SECOND-ORDER ASYMPTOTIC TANGENT CONES 187
4.13 SECOND-ORDER INVERSION THEOREMS 192
4.14 EXPRESSIONS OF THE SECOND-ORDER CONTINGENT SET
ON SPECIFIC CONSTRAINTS 197
4.15 MISCELLANEOUS SECOND-ORDER TANGENT CONES 202
4.15.1 SECOND-ORDER TANGENT CONES OF LEDZEWICZ
AND SCHAETTLER 202
4.15.2 PROJECTIVE TANGENT CONES OF SECOND-ORDER 204
4.15.3 SECOND-ORDER TANGENT CONE OF N. PAVEL 206
4.15.4 CONNECTIONS AMONG THE SECOND-ORDER
TANGENT CONES 207
4.16 SECOND-ORDER LOCAL APPROXIMATION 207
4.17 HIGHER-ORDER TANGENT CONES AND TANGENT SETS 210
5 NONCONVEX SEPARATION THEOREMS 213
5.1 SEPARATING FUNCTIONS AND EXAMPLES 213
5.2 NONLINEAR SEPARATION 217
5.2.1 CONSTRUCTION OF SCALARIZING FUNCTIONALS 217
5.2.2 PROPERTIES OF SCALARIZATION FUNCTIONS 219
5.2.3 CONTINUITY PROPERTIES 224
5.2.4 LIPSCHITZ PROPERTIES 225
5.2.5 THE FORMULA FOR THE CONJUGATE
AND SUBDIFFERENTIAL OF PA FOR
A CONVEX 231
5.3 SCALARIZING FUNCTIONALS BY HIRIART-URRUTY AND ZAFFARONI 232
5.4 CHARACTERIZATION OF SOLUTIONS OF SET-VALUED
OPTIMIZATION PROBLEMS BY MEANS OF NONLINEAR
SCALARIZING FUNCTIONALS 236
5.4.1 AN EXTENSION OF THE FUNCTIONAL PT 236
5.4.2 CHARACTERIZATION OF SOLUTIONS OF SET-VALUED
OPTIMIZATION PROBLEMS WITH LOWER SET LESS
ORDER RELATION
LC
BY SCALARIZATION 240
5.5 THE EXTREMAL PRINCIPLE 244
6 HAHN-BANACH "TYPE THEOREMS 249
6.1 THE HAHN-BANACH-KANTOROVICH THEOREM 250
6.2 CLASSICAL SEPARATION THEOREMS FOR CONVEX SETS 258
6.3 THE CORE CONVEX TOPOLOGY 261
6.4 YANG'S GENERALIZATION OF THE HAHN-BANACH THEOREM 264
6.5 A SUFFICIENT CONDITION FOR THE CONVEXITY OF M+ A 271
XVI
CONTENTS
7 CONJUGATES AND SUBDIFFERENTIALS 275
7.1 THE STRONG CONJUGATE AND SUBDIFFERENTIAL 275
7.2 THE WEAK SUBDIFFERENTIAL 288
7.3 SUBDIFFERENTIALS CORRESPONDING TO HENIG PROPER EFFICIENCY 296
7.4 EXACT FORMULAS FOR THE SUBDIFFERENTIAL OF THE SUM
AND THE COMPOSITION 298
8 DUALITY 307
8.1 DUALITY ASSERTIONS FOR SET-VALUED PROBLEMS BASED
ON VECTOR APPROACH 308
8.1.1 CONJUGATE DUALITY FOR SET-VALUED PROBLEMS
BASED ON VECTOR APPROACH 308
8.1.2 LAGRANGE DUALITY FOR SET-VALUED
OPTIMIZATION PROBLEMS BASED ON VECTOR APPROACH 313
8.2 DUALITY ASSERTIONS FOR SET-VALUED PROBLEMS BASED
ON SET APPROACH 317
8.3 DUALITY ASSERTIONS FOR SET-VALUED PROBLEMS BASED
ON LATTICE STRUCTURE 322
8.3.1 CONJUGATE DUALITY FOR ^"-VALUED PROBLEMS 323
8.3.2 LAGRANGE DUALITY FOR J^-VALUED PROBLEMS 326
8.4 COMPARISON OF DIFFERENT APPROACHES TO DUALITY
IN SET-VALUED OPTIMIZATION 338
8.4.1 LAGRANGE DUALITY 339
8.4.2 SUBDIFFERENTIALS AND STABILITY 341
8.4.3 DUALITY STATEMENTS WITH OPERATORS AS DUAL VARIABLES. 345
9 EXISTENCE RESULTS FOR MINIMAL POINTS 349
9.1 PRELIMINARY NOTIONS AND RESULTS CONCERNING
TRANSITIVE RELATIONS 349
9.2 EXISTENCE OF MINIMAL ELEMENTS WITH RESPECT
TO TRANSITIVE RELATIONS 352
9.3 EXISTENCE OF MINIMAL POINTS WITH RESPECT TO CONES 355
9.4 TYPES OF CONVEX CONES AND COMPACTNESS
WITH RESPECT TO CONES 360
9.5 EXISTENCE OF OPTIMAL SOLUTIONS FOR VECTOR AND SET
OPTIMIZATION PROBLEMS 362
10 EKELAND VARIATIONAL PRINCIPLE 369
10.1 PRELIMINARY NOTIONS AND RESULTS 369
10.2 MINIMAL POINTS IN PRODUCT SPACES 373
10.3 MINIMAL POINTS IN PRODUCT SPACES OF ISAC-TAMMER'S TYPE 381
10.4 EKELAND'S VARIATIONAL PRINCIPLES OF HA'S TYPE 384
10.5 EKELAND'S VARIATIONAL PRINCIPLE FOR BI-SET-VALUED MAPS 390
10.6 EVP TYPE RESULTS 391
10.7 ERROR BOUNDS 394
CONTENTS XVII
11 DERIVATIVES AND EPIDERIVATIVES OF SET-VALUED MAPS 399
11.1 CONTINGENT DERIVATIVES OF SET-VALUED MAPS 400
11.1.1 MISCELLANEOUS GRAPHICAL DERIVATIVES
OF SET-VALUED MAPS 407
11.1.2 CONVEXITY CHARACTERIZATION USING
CONTINGENT DERIVATIVES 414
11.1.3 PROTO-DIFFERENTIABILITY,
SEMI-DIFFERENTIABILITY, AND RELATED
CONCEPTS 416
11.1.4 WEAK CONTINGENT DERIVATIVES OF SET-VALUED MAPS 422
11.1.5 A LYUSTERNIK-TYPE THEOREM USING
CONTINGENT DERIVATIVES 426
11.2 CALCULUS RULES FOR DERIVATIVES OF SET-VALUED MAPS 428
11.2.1 CALCULUS RULES BY A DIRECT APPROACH 429
11.2.2 DERIVATIVE RULES BY USING CALCULUS
OF TANGENT CONES 432
11.3 CONTINGENTLY C-ABSORBING MAPS 437
11.4 EPIDERIVATIVES OF SET-VALUED MAPS 445
11.4.1 CONTINGENT EPIDERIVATIVES OF SET-VALUED
MAPS WITH IMAGES IN R 446
11.4.2 CONTINGENT EPIDERIVATIVES IN GENERAL SPACES 452
11.4.3 EXISTENCE THEOREMS FOR CONTINGENT EPIDERIVATIVES 457
11.4.4 VARIATIONAL CHARACTERIZATION
OF THE CONTINGENT EPIDERIVATIVES 464
11.5 GENERALIZED CONTINGENT EPIDERIVATIVES OF SET-VALUED MAPS 470
11.5.1 EXISTENCE THEOREMS FOR GENERALIZED
CONTINGENT EPIDERIVATIVES 474
11.5.2 CHARACTERIZATIONS OF GENERALIZED CONTINGENT
EPIDERIVATIVES 478
11.6 CALCULUS RULES FOR CONTINGENT EPIDERIVATIVES 482
11.7 SECOND-ORDER DERIVATIVES OF SET-VALUED MAPS 488
11.8 CALCULUS RULES FOR SECOND-ORDER CONTINGENT DERIVATIVES 500
11.9 SECOND-ORDER EPIDERIVATIVES OF SET-VALUED MAPS 504
12 OPTIMALITY CONDITIONS IN SET-VALUED OPTIMIZATION 509
12.1 FIRST-ORDER OPTIMALITY CONDITIONS BY THE DIRECT APPROACH 512
12.2 FIRST-ORDER OPTIMALITY CONDITIONS
BY THE DUBOVITSKII-MILYUTIN APPROACH 522
12.2.1 NECESSARY OPTIMALITY CONDITIONS
BY THE DUBOVITSKII-MILYUTIN APPROACH 523
12.2.2 INVERSE IMAGES AND SUBGRADIENTS
OF SET-VALUED MAPS 527
12.2.3 SEPARATION THEOREMS
AND THE DUBOVITSKII-MILYUTIN LEMMA 534
XVIII
CONTENTS
12.2.4 LAGRANGE MULTIPLIER RULES
BY THE DUBOVITSKII-MILYUTIN APPROACH 537
12.3 SUFFICIENT OPTIMALITY CONDITIONS IN SET-VALUED OPTIMIZATION. 542
12.3.1 SUFFICIENT OPTIMALITY CONDITIONS UNDER
CONVEXITY AND QUASI-CONVEXITY 542
12.3.2 SUFFICIENT OPTIMALITY CONDITIONS UNDER
PARACONVEXITY 545
12.3.3 SUFFICIENT OPTIMALITY CONDITIONS UNDER
SEMIDIFFERENTIABILITY 549
12.4 SECOND-ORDER OPTIMALITY CONDITIONS IN SET-VALUED
OPTIMIZATION 549
12.4.1 SECOND-ORDER OPTIMALITY CONDITIONS
BY THE DUBOVITSKII-MILYUTIN APPROACH 550
12.4.2 SECOND-ORDER OPTIMALITY CONDITIONS
BY THE DIRECT APPROACH 554
12.5 GENERALIZED DUBOVITSKII-MILYUTIN APPROACH
IN SET-VALUED OPTIMIZATION 557
12.5.1 A SEPARATION THEOREM FOR MULTIPLE CLOSED
AND OPEN CONES 559
12.5.2 FIRST-ORDER GENERALIZED
DUBOVITSKII-MILYUTIN APPROACH 562
12.5.3 SECOND-ORDER GENERALIZED
DUBOVITSKII-MILYUTIN APPROACH 567
12.6 SET-VALUED OPTIMIZATION PROBLEMS WITH A VARIABLE
ORDER STRUCTURE 568
12.7 OPTIMALITY CONDITIONS FOR Q-MINIMIZERS
IN SET-VALUED OPTIMIZATION 572
12.7.1 OPTIMALITY CONDITIONS FOR Q-MINIMIZERS
USING RADIAL DERIVATIVES 572
12.7.2 OPTIMALITY CONDITIONS FOR Q-MINIMIZERS
USING CODERIVATIVES 574
12.8 LAGRANGE MULTIPLIER RULES BASED ON LIMITING SUBDIFFERENTIAL. 578
12.9 NECESSARY CONDITIONS FOR APPROXIMATE SOLUTIONS
OF SET-VALUED OPTIMIZATION PROBLEMS 591
12.10 NECESSARY AND SUFFICIENT CONDITIONS FOR SOLUTION
CONCEPTS BASED ON SET APPROACH 594
12.11 NECESSARY CONDITIONS FOR SOLUTION CONCEPTS
WITH RESPECT TO A GENERAL PREFERENCE RELATION 598
12.12 KKT-POINTS AND CORRESPONDING STABILITY RESULTS 600
13 SENSITIVITY ANALYSIS IN SET-VALUED OPTIMIZATION
AND VECTOR VARIATIONAL INEQUALITIES 605
13.1 FIRST ORDER SENSITIVITY ANALYSIS IN SET-VALUED OPTIMIZATION 606
13.2 SECOND ORDER SENSITIVITY ANALYSIS IN SET-VALUED
OPTIMIZATION 613
CONTENTS XIX
13.3 SENSITIVITY ANALYSIS IN SET-VALUED OPTIMIZATION
USING CODERIVATIVES 623
13.4 SENSITIVITY ANALYSIS FOR VECTOR VARIATIONAL INEQUALITIES 634
14 NUMERICAL METHODS FOR SOLVING SET-VALUED
OPTIMIZATION PROBLEMS 645
14.1 A NEWTON METHOD FOR SET-VALUED MAPS 645
14.2 AN ALGORITHM TO SOLVE POLYHEDRAL CONVEX SET-VALUED
OPTIMIZATION PROBLEMS 651
14.2.1 FORMULATION OF THE POLYHEDRAL CONVEX
SET-VALUED OPTIMIZATION PROBLEM 653
14.2.2 AN ALGORITHM FOR SOLVING POLYHEDRAL
CONVEX SET-VALUED OPTIMIZATION PROBLEMS 655
14.2.3 PROPERTIES OF THE ALGORITHM 658
15 APPLICATIONS 663
15.1 SET-VALUED APPROACHES TO DUALITY IN VECTOR OPTIMIZATION 663
15.1.1 FENCHEL DUALITY FOR VECTOR OPTIMIZATION
PROBLEMS USING CORRESPONDING RESULTS
FOR ^"-VALUED PROBLEMS 667
15.1.2 LAGRANGE DUALITY FOR VECTOR OPTIMIZATION
PROBLEMS BASED ON RESULTS FOR ^-VALUED PROBLEMS 670
15.1.3 DUALITY ASSERTIONS FOR LINEAR VECTOR
OPTIMIZATION BASED ON LATTICE APPROACH 677
15.1.4 FURTHER SET-VALUED APPROACHES TO DUALITY
IN LINEAR VECTOR OPTIMIZATION 682
15.2 APPLICATIONS IN MATHEMATICAL FINANCE 696
15.3 SET-VALUED OPTIMIZATION IN WELFARE ECONOMICS 701
15.4 ROBUSTNESS FOR VECTOR-VALUED OPTIMIZATION PROBLEMS 706
15.4.1
U
R-ROBUSTNESS 710
15.4.2 ^-ROBUSTNESS 720
15.4.3 ^-ROBUSTNESS 722
15.4.4 ALGORITHMS FOR SOLVING SPECIAL CLASSES
OF SET-VALUED OPTIMIZATION PROBLEMS 724
APPENDIX 727
REFERENCES 733
INDEX
759 |
| any_adam_object | 1 |
| author | Khan, Akhtar A. Tammer, Christiane 1955- Zălinescu, Constantin 1952- |
| author_GND | (DE-588)1106856139 (DE-588)112846955 (DE-588)1146393032 |
| author_facet | Khan, Akhtar A. Tammer, Christiane 1955- Zălinescu, Constantin 1952- |
| author_role | aut aut aut |
| author_sort | Khan, Akhtar A. |
| author_variant | a a k aa aak c t ct c z cz |
| building | Verbundindex |
| bvnumber | BV043424289 |
| classification_rvk | SK 870 |
| ctrlnum | (OCoLC)869473744 (DE-599)DNB1046584243 |
| dewey-full | 519.6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.6 |
| dewey-search | 519.6 |
| dewey-sort | 3519.6 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV043424289 |
| illustrated | Not Illustrated |
| indexdate | 2024-08-03T02:55:00Z |
| institution | BVB |
| isbn | 9783642542640 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028842163 |
| oclc_num | 869473744 |
| open_access_boolean | |
| owner | DE-29T DE-20 DE-11 DE-83 DE-188 |
| owner_facet | DE-29T DE-20 DE-11 DE-83 DE-188 |
| physical | xxii, 765 Seiten Diagramme |
| publishDate | 2015 |
| publishDateSearch | 2015 |
| publishDateSort | 2015 |
| publisher | Springer |
| record_format | marc |
| series2 | Vector optimization |
| spelling | Khan, Akhtar A. Verfasser (DE-588)1106856139 aut Set-valued optimization an introduction with applications Akhtar A. Khan, Christiane Tammer, Constantin Zălinescu Heidelberg ; New York ; Dordrecht ; London Springer [2015] © 2015 xxii, 765 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Vector optimization Dualitätstheorie (DE-588)4150801-4 gnd rswk-swf Mengenwertige Abbildung (DE-588)4270772-9 gnd rswk-swf Optimierung (DE-588)4043664-0 gnd rswk-swf Research cone properties Hahn-Banach extension nonconvex separation existence theorem minimal point variational analysis Dualitätstheorie (DE-588)4150801-4 s Optimierung (DE-588)4043664-0 s Mengenwertige Abbildung (DE-588)4270772-9 s 1\p DE-604 Tammer, Christiane 1955- Verfasser (DE-588)112846955 aut Zălinescu, Constantin 1952- Verfasser (DE-588)1146393032 aut Erscheint auch als Online-Ausgabe 978-3-642-54265-7 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4570881&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028842163&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Khan, Akhtar A. Tammer, Christiane 1955- Zălinescu, Constantin 1952- Set-valued optimization an introduction with applications Dualitätstheorie (DE-588)4150801-4 gnd Mengenwertige Abbildung (DE-588)4270772-9 gnd Optimierung (DE-588)4043664-0 gnd |
| subject_GND | (DE-588)4150801-4 (DE-588)4270772-9 (DE-588)4043664-0 |
| title | Set-valued optimization an introduction with applications |
| title_auth | Set-valued optimization an introduction with applications |
| title_exact_search | Set-valued optimization an introduction with applications |
| title_full | Set-valued optimization an introduction with applications Akhtar A. Khan, Christiane Tammer, Constantin Zălinescu |
| title_fullStr | Set-valued optimization an introduction with applications Akhtar A. Khan, Christiane Tammer, Constantin Zălinescu |
| title_full_unstemmed | Set-valued optimization an introduction with applications Akhtar A. Khan, Christiane Tammer, Constantin Zălinescu |
| title_short | Set-valued optimization |
| title_sort | set valued optimization an introduction with applications |
| title_sub | an introduction with applications |
| topic | Dualitätstheorie (DE-588)4150801-4 gnd Mengenwertige Abbildung (DE-588)4270772-9 gnd Optimierung (DE-588)4043664-0 gnd |
| topic_facet | Dualitätstheorie Mengenwertige Abbildung Optimierung |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=4570881&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028842163&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT khanakhtara setvaluedoptimizationanintroductionwithapplications AT tammerchristiane setvaluedoptimizationanintroductionwithapplications AT zalinescuconstantin setvaluedoptimizationanintroductionwithapplications |