Verfügbarkeit: Theory of extremal problems | Technische Universität München

Theory of extremal problems:

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Bibliographische Detailangaben
Beteiligte Personen:	Ioffe, Aleksandr D. 1938- (VerfasserIn), Tichomirov, Vladimir M. (VerfasserIn)
Format:	Buch
Sprache:	Englisch Russisch
Veröffentlicht:	Amsterdam [u.a.] North-Holland Publ. 1979
Schriftenreihe:	Studies in mathematics and its applications 6
Schlagwörter:	Calcul des variations Maximums et minimums Optimisation mathématique Calculus of variations Extremal problems (Mathematics) Mathematical optimization Maxima and minima Optimierung Variationsrechnung Extremwert
Links:	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
Beschreibung:	Aus dem Russ. übers.
Umfang:	XII, 460 S.
ISBN:	0444851674

Internformat

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Datensatz im Suchindex

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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	2024-12-20T07:48:25Z
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
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physical	XII, 460 S.
publishDate	1979
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publisher	North-Holland Publ.
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series	Studies in mathematics and its applications
series2	Studies in mathematics and its applications
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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Signatur:	0102 MAT 492f 2001 A 19081 Lageplan 0102 MAT 492f 2001 A 19082 Lageplan
Exemplar 1	Ausleihbar Am Standort
Exemplar 2	Ausleihbar Am Standort