Theory of extremal problems:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English Russian |
| Veröffentlicht: |
Amsterdam [u.a.]
North-Holland Publ.
1979
|
| Schriftenreihe: | Studies in mathematics and its applications
6 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Aus dem Russ. übers. |
| Beschreibung: | XII, 460 S. |
| ISBN: | 0444851674 |
Internformat
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| 100 | 1 | |a Ioffe, Aleksandr D. |d 1938- |e Verfasser |0 (DE-588)109388127 |4 aut | |
| 240 | 1 | 0 | |a Teorija ėkstremal'nych zadač |
| 245 | 1 | 0 | |a Theory of extremal problems |c A. D. Ioffe ; V. M. Tihomirov |
| 264 | 1 | |a Amsterdam [u.a.] |b North-Holland Publ. |c 1979 | |
| 300 | |a XII, 460 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Studies in mathematics and its applications |v 6 | |
| 500 | |a Aus dem Russ. übers. | ||
| 650 | 4 | |a Calcul des variations | |
| 650 | 4 | |a Maximums et minimums | |
| 650 | 4 | |a Optimisation mathématique | |
| 650 | 4 | |a Calculus of variations | |
| 650 | 4 | |a Extremal problems (Mathematics) | |
| 650 | 4 | |a Mathematical optimization | |
| 650 | 4 | |a Maxima and minima | |
| 650 | 0 | 7 | |a Optimierung |0 (DE-588)4043664-0 |2 gnd |9 rswk-swf |
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| 700 | 1 | |a Tichomirov, Vladimir M. |e Verfasser |4 aut | |
| 830 | 0 | |a Studies in mathematics and its applications |v 6 |w (DE-604)BV000000646 |9 6 | |
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Datensatz im Suchindex
| _version_ | 1804116713181020160 |
|---|---|
| adam_text | CONTENTS
Preface v
Basic notation vjjj
0. INTRODUCTION. BACKGROUND MATERIAL 1
0.1 Functional analysis 12
0.2 Differential calculus 22
0.3 Convex analysis 44
0.4 Differential equations 50
CHAPTER 1. NECESSARY CONDITIONS FOR AN EXTREMUM 65
1.1 Statements of the problems and formulations of basic theorems 65
1.2 Smooth problems. The Lagrange multiplier rule 77
1.3 Convex problems. Proof of the Kuhn Tucker theorem 80
1.4 Mixed problems. Proof of the extremal principle 84
CHAPTER 2. NECESSARY CONDITIONS FOR AN EXTREMUM
IN THE CLASSICAL PROBLEMS OF THE CAL¬
CULUS OF VARIATIONS AND OPTIMAL CON¬
TROL 93
2.1 Statements of the problems 93
2.2 Elementary derivation of necessary conditions for an extremum in simplest
problems of the classical calculus of variations 101
2.3 The Lagrange problem. The Euler, Lagrange equation 124
2.4 The Pontrjagin maximum principle. Formulation and discussion 132
2.5 Proof of the maximum principle 147
CHAPTER 3. ELEMENTS OF CONVEX ANALYSIS 161
3.1 Convex sets and separation theorems 161
3.2 Convex functions 167
3.3 Conjugate functions. The Fenchel Moreau theorem 171
3.4 Duality theorems 178
3.5 Convex analysis in finite dimensional spaces 184
CHAPTER 4. LOCAL CONVEX ANALYSIS 191
4.1 Homogeneous functions and directional derivatives 191
4.2 Subdifferentials. Basic theorems 196
xi
xii CONTENTS
4.3 Cones of supporting functionals 205
4.4 Locally convex functions 208
4.5 The subdifferentials of certain functions 216
CHAPTER 5. LOCALLY CONVEX PROBLEMS AND THE
MAXIMUM PRINCIPLE FOR PROBLEMS WITH
PHASE CONSTRAINTS , 224
5.1 Locally convex problems 224
5.2 Optimal control problems with phase constraints 233
5.3 Proof of the maximum principle for problems with phase constraints . . . . 241
CHAPTER 6. SPECIAL PROBLEMS 255
6.1 Linear programming 255
6.2 The theory of quadratic forms in Hilbert space 258
6.3 Quadratic functionals in the classical caculus of variations 266
6.4 Discrete optimal control problems 277
CHAPTER 7. SUFFICIENT CONDITIONS FOR AN EXTREMUM 284
7.1 The perturbation method 284
7.2 Smooth problems 290
7.3 Convex problems 299
7.4 Sufficient conditions for an extremum in the classical calculus of variations . . 303
CHAPTER 8. MEASURABLE MULTIMAPPINGS AND CONVEX
ANALYSIS OF INTEGRAL FUNCTIONALS ... 321
8.1 Multimappings and measurability 321
8.2 Integration of multimappings 334
8.3 Integral functionals 340
CHAPTER 9. EXISTENCE OF SOLUTIONS IN PROBLEMS
OF THE CALCULUS OF VARIATIONS AND OPTI¬
MAL CONTROL 354
9.1 Semicontinuity of the functionals in the calculus of variations and the compact¬
ness of their level sets 354
9.2 Theorems on the existence of solutions 369
9.3 The convolution integral and linear problems 385
CHAPTER 10. APPLICATION OF THE THEORY TO SPECIFIC
PROBLEMS 404
10.1 Problems in geometric optics 404
10.2 Young s inequality and Helly s theorem 414
10.3 Optimal excitation of an oscillator 418
Problems 423
Bibliography . 443
Subject Index 457
|
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| author | Ioffe, Aleksandr D. 1938- Tichomirov, Vladimir M. |
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| id | DE-604.BV002256385 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:42:53Z |
| institution | BVB |
| isbn | 0444851674 |
| language | English Russian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001482734 |
| oclc_num | 3912607 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-384 DE-703 DE-355 DE-BY-UBR DE-824 DE-19 DE-BY-UBM DE-706 DE-83 DE-188 |
| owner_facet | DE-91G DE-BY-TUM DE-384 DE-703 DE-355 DE-BY-UBR DE-824 DE-19 DE-BY-UBM DE-706 DE-83 DE-188 |
| physical | XII, 460 S. |
| publishDate | 1979 |
| publishDateSearch | 1979 |
| publishDateSort | 1979 |
| publisher | North-Holland Publ. |
| record_format | marc |
| series | Studies in mathematics and its applications |
| series2 | Studies in mathematics and its applications |
| spelling | Ioffe, Aleksandr D. 1938- Verfasser (DE-588)109388127 aut Teorija ėkstremal'nych zadač Theory of extremal problems A. D. Ioffe ; V. M. Tihomirov Amsterdam [u.a.] North-Holland Publ. 1979 XII, 460 S. txt rdacontent n rdamedia nc rdacarrier Studies in mathematics and its applications 6 Aus dem Russ. übers. Calcul des variations Maximums et minimums Optimisation mathématique Calculus of variations Extremal problems (Mathematics) Mathematical optimization Maxima and minima Optimierung (DE-588)4043664-0 gnd rswk-swf Variationsrechnung (DE-588)4062355-5 gnd rswk-swf Extremwert (DE-588)4137272-4 gnd rswk-swf Variationsrechnung (DE-588)4062355-5 s Optimierung (DE-588)4043664-0 s DE-604 Extremwert (DE-588)4137272-4 s Tichomirov, Vladimir M. Verfasser aut Studies in mathematics and its applications 6 (DE-604)BV000000646 6 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001482734&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ioffe, Aleksandr D. 1938- Tichomirov, Vladimir M. Theory of extremal problems Studies in mathematics and its applications Calcul des variations Maximums et minimums Optimisation mathématique Calculus of variations Extremal problems (Mathematics) Mathematical optimization Maxima and minima Optimierung (DE-588)4043664-0 gnd Variationsrechnung (DE-588)4062355-5 gnd Extremwert (DE-588)4137272-4 gnd |
| subject_GND | (DE-588)4043664-0 (DE-588)4062355-5 (DE-588)4137272-4 |
| title | Theory of extremal problems |
| title_alt | Teorija ėkstremal'nych zadač |
| title_auth | Theory of extremal problems |
| title_exact_search | Theory of extremal problems |
| title_full | Theory of extremal problems A. D. Ioffe ; V. M. Tihomirov |
| title_fullStr | Theory of extremal problems A. D. Ioffe ; V. M. Tihomirov |
| title_full_unstemmed | Theory of extremal problems A. D. Ioffe ; V. M. Tihomirov |
| title_short | Theory of extremal problems |
| title_sort | theory of extremal problems |
| topic | Calcul des variations Maximums et minimums Optimisation mathématique Calculus of variations Extremal problems (Mathematics) Mathematical optimization Maxima and minima Optimierung (DE-588)4043664-0 gnd Variationsrechnung (DE-588)4062355-5 gnd Extremwert (DE-588)4137272-4 gnd |
| topic_facet | Calcul des variations Maximums et minimums Optimisation mathématique Calculus of variations Extremal problems (Mathematics) Mathematical optimization Maxima and minima Optimierung Variationsrechnung Extremwert |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001482734&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000646 |
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