Convexity and optimization in Banach spaces:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Bucureşti
Ed. Acad. u.a.
1986
|
| Edition: | 2., rev. and extended ed. |
| Series: | Mathematics and its applications / East European series
10 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | EST: Convexitate şi optimizare in spaţii Banach <engl.>. - Aus d. Rumän. übers. |
| Physical Description: | XVII, 397 S. |
| ISBN: | 9027717613 |
Staff View
MARC
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| 264 | 1 | |a Bucureşti |b Ed. Acad. u.a. |c 1986 | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Editor s Preface ix
Preface to the first edition xiii
Preface to the English edition xv
Preface to the second English edition xvii
CHAPTEK 1
Fundamentals of functional analysis
§ 1. Convexity in topological linear spaees
1.1. Classes of topological linear spaces 1
1.2. Convex sets 8
1.3. Separation of convex sets 15
1.4. Closedness of the sum of two sets 25
§ 2. Duality in linear normed spaces
2.1. The dual systems of linear spaces 29
2.2. Weak topologies on linear normed spaces ... 32
2.3. Reflexive Banach spaces 38
2.4. Duality mapping 41
§ 3. Vector valued functions and distributions
3.1. The Bochner integral 49
3.2. Bounded variation vector functions 51
3.3. Vector measures and distributions on real intervals 53
3.4. Sobolev spaces 63
§ 4. Maximal monotone operators and evolution systems in
Banaeh spaces
4.1. Definitions and fundamental results 65
4.2. Linear evolution equations in Banach spaees . . 72
vi CONTKNTS
CHAPTBE 2
Convex functions
§ 1. General properties of convex functions
1.1. Definitions and basic properties . 83
1.2. Lower semicontinuous functions 86
1.3. Lower semieontinuous convex functions .... 88
1.4. Conjugate functions 93
§ 2. The subdifferential of a convex function
2.1. Definition and fundamental results ...... 101
2.2. Further properties of subdifferential mappings . . 108
2.3. Regularization of the convex function 120
2.4. Perturbation of cyclically monotone operators
and .subdifferential calculus 124
2.5. Variational inequalities 132
2.6. Further extensions of the concept of gradient . . . 142
§ 3. Concave convex functions
3.1. Saddle points and minimax equality 145
3.2. Saddle functions *.... .. 147
3.3. Minimax theorems 159
Bibliographical notes 169
CHAPTEK 3
Convex programming
§ 1. Optimality conditions
1.1. The case of a finite number of constraints .... 171
1.2. Operatorial convex constraints 178
1.3. JTon linear programming in the case of Frechet
differentiability 185
§ 2. Duality in convex programming
2.1. Dual problems 196
2.2. Fenchel duality theorem 203
2.3. Optimality through closedness 209
2.4. Examples . . 218
CONTENTS vii
§ 3. Applications of the duality theory
3.1. Linear programming 230
3.2. The best approximation problem 235
Bibliographical notes 242
CHAPTER 4
Convex control problems in Bunach spaces
§ 1. Distributed control convex problems
1.1. Formulation of the problem and basic assumptions 247
1.2. Existence of optimal arcs 254
1.3. The maximum principle 258
1.4. Proof of Theorem 1.1 262
1.5. Proof of Theorem 1.2 280
1.6. Further remarks on optimality theorems .... 284
1.7. The dual control problem . 290
1.8. Some examples 296
§ 2. Synthesis of optimal control
2.1. Optimal value function and existence of optimal
synthesis 313
2.2. Hamilton Jacobi equations 319
§ 3. Convex control problems with infinite time horizon 335
3.1. Formulation of the problem. Existence 335
3.2. Optimal feedback controls 339
3.3. The Hamiltonian conditions for optimality . . . 345
3.4. The linear quadratic regulator problem 353
§ 4. Boundary control problems with conve.r cost criteria
4.1. Boundary control systems 357
4.2. Formulation of the problem and the main result 362
4.3. Proof of the main result 366
Bibliographical notes 371
Bibliography 375
Symbols used 393
Subject index 395
|
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| author | Barbu, Viorel Precupanu, Teodor |
| author_facet | Barbu, Viorel Precupanu, Teodor |
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| author_sort | Barbu, Viorel |
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| bvnumber | BV000531187 |
| classification_rvk | SK 600 |
| classification_tum | MAT 915f MAT 462f |
| ctrlnum | (OCoLC)631043100 (DE-599)BVBBV000531187 |
| discipline | Mathematik |
| edition | 2., rev. and extended ed. |
| format | Book |
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| id | DE-604.BV000531187 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:15:18Z |
| institution | BVB |
| isbn | 9027717613 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000327706 |
| oclc_num | 631043100 |
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| physical | XVII, 397 S. |
| publishDate | 1986 |
| publishDateSearch | 1986 |
| publishDateSort | 1986 |
| publisher | Ed. Acad. u.a. |
| record_format | marc |
| series2 | Mathematics and its applications / East European series |
| spelling | Barbu, Viorel Verfasser aut Convexity and optimization in Banach spaces V. Barbu and Th. Precupanu 2., rev. and extended ed. Bucureşti Ed. Acad. u.a. 1986 XVII, 397 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications / East European series 10 EST: Convexitate şi optimizare in spaţii Banach <engl.>. - Aus d. Rumän. übers. Optimierung (DE-588)4043664-0 gnd rswk-swf Konvexität (DE-588)4114284-6 gnd rswk-swf Banach-Raum (DE-588)4004402-6 gnd rswk-swf Konvexe Optimierung (DE-588)4137027-2 gnd rswk-swf Banach-Raum (DE-588)4004402-6 s Konvexität (DE-588)4114284-6 s Optimierung (DE-588)4043664-0 s Konvexe Optimierung (DE-588)4137027-2 s 1\p DE-604 DE-604 Precupanu, Teodor Verfasser aut East European series Mathematics and its applications 10 (DE-604)BV000006709 10 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000327706&sequence=000002&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 | Barbu, Viorel Precupanu, Teodor Convexity and optimization in Banach spaces Optimierung (DE-588)4043664-0 gnd Konvexität (DE-588)4114284-6 gnd Banach-Raum (DE-588)4004402-6 gnd Konvexe Optimierung (DE-588)4137027-2 gnd |
| subject_GND | (DE-588)4043664-0 (DE-588)4114284-6 (DE-588)4004402-6 (DE-588)4137027-2 |
| title | Convexity and optimization in Banach spaces |
| title_auth | Convexity and optimization in Banach spaces |
| title_exact_search | Convexity and optimization in Banach spaces |
| title_full | Convexity and optimization in Banach spaces V. Barbu and Th. Precupanu |
| title_fullStr | Convexity and optimization in Banach spaces V. Barbu and Th. Precupanu |
| title_full_unstemmed | Convexity and optimization in Banach spaces V. Barbu and Th. Precupanu |
| title_short | Convexity and optimization in Banach spaces |
| title_sort | convexity and optimization in banach spaces |
| topic | Optimierung (DE-588)4043664-0 gnd Konvexität (DE-588)4114284-6 gnd Banach-Raum (DE-588)4004402-6 gnd Konvexe Optimierung (DE-588)4137027-2 gnd |
| topic_facet | Optimierung Konvexität Banach-Raum Konvexe Optimierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000327706&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000006709 |
| work_keys_str_mv | AT barbuviorel convexityandoptimizationinbanachspaces AT precupanuteodor convexityandoptimizationinbanachspaces |