Quasidifferentiability and nonsmooth modelling in mechanics, engineering and economics:
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Dordrecht [u.a.]
Kluwer
1996
|
| Schriftenreihe: | Nonconvex optimization and its applications
10 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVII, 348 S. graph. Darst. |
| ISBN: | 0792340930 |
Internformat
MARC
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| 650 | 4 | |a Engineering |x Mathematical models | |
| 650 | 4 | |a Mechanics, Applied |x Mathematical models | |
| 650 | 4 | |a Nonsmooth optimization | |
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Datensatz im Suchindex
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| adam_text | QUASIDIFFERENTIABILITY AND NONSMOOTH MODELLING IN MECHANICS, ENGINEERING
AND ECONOMICS BY VLADIMIR F. DEM YANOV DEPARTMENT OF MATHEMATICS, ST.
PETERSBURG STATE UNIVERSITY, ST. PETERSBURG, RUSSIA GEORGIOS E.
STAVROULAKIS LEHR- UND FORSCHUNGSGEBIET FUR MECHANIK; LEHRSTUHL CFIIR
MATHEMATIK, RWTH, AACHEN, GERMANY LUDMILA N. POLYAKOVA DEPARTMENT OF
MATHEMATICS, ST. PETERSBURG STATE UNIVERSITY, ST. PETERSBURG, RUSSIA AND
PANAGIOTIS D. PANAGIOTOPOULOS DEPARTMENT OF CIVIL ENGINEERING, ARISTOTLE
UNIVERSITY, THESSALONIKI, GREECE; AND FACULTY OF MATHEMATICS AND
PHYSICS, RWTH, AACHEN, GERMANY KLUWER ACADEMIC PUBLISHERS DORDRECHT /
BOSTON / LONDON TABLE OF CONTENTS PREFACE XL INTRODUCTION I XIII
GUIDELINES FOR THE READERS XV 1. NONSMOOTH ANALYSIS THE ONE*DIMENSIONAL
CASE 1 1.1 ONE-SIDED DERIVATIVES 1 1.2 CALCULUS OF QUASIDIFFERENTIALS 7
1.3 THE DIRECTIONAL DIFFERENTIABILITY OF A COMPOSITION 10 1.4 THE
CONTINUITY OF A QUASIDIFFERENTIAL MAPPING 16 1.5 CODIFFERENTIABLE
FUNCTIONS 18 1.6 THE CODIFFERENTIABILITY OF A PIECE-WISE SMOOTH FUNCTION
22 1.7 THE K-TH ORDER CODIFFERENTIABILITY 36 1.8 THE DINI DERIVATIVES 39
1.9 THE CLARKE DERIVATIVES 45 REFERENCES OF CHAPTER 1 48 I 2.
QUASIDIFFERENTIABLE FUNCTIONS AND SETS QUASIDIFFERENTIABLE OPTIMIZATION
AND OPTIMALITY CONDITIONS 49 2.1 HOMOGENEOUS APPROXIMATIONS OF SETS,
FUNCTIONS AND MAPPINGS 49 2.1.1 CONICAL APPROXIMATION OF SETS 49 2.1.2
DINI AND HADAMARD DERIVATIVES AND THEIR PROPERTIES .. 53 2.1.3
PROPERTIES OF DINI AND HADAMARD DERIVATIVES 57 2.1.4 SETS DEFINED BY
INEQUALITIES AND EQUATIONS. APPROXIMATION AND REGULARITY CONDITIONS 59
2.2 QUASIDIFFERENTIABLE FUNCTIONS 61 2.2.1 DIFFERENCE OF CONVEX COMPACT
SETS 61 2 .2.2 QUASIDIFFERENTIABLE FUNCTIONS. QUASIDIFFERENTIAL CALCULUS
66 2.2.3 SETS DEFINED BY QUASIDIFFERENTIABLE FUNCTIONS: GENERAL POSITION
AND REGULARITY CONDITIONS 69 VI TABLE OF CONTENTS 22A STAR-SHAPED SETS
AND QUASIDIFFERENTIABILITY 70 2.2.5 CHOOSING THE BEST QUASIDIFFERENTIAL
72 2.2.6 UPPER CONVEX AND LOWER CONCAVE APPROXIMATIONS OF FUNCTIONS 73
2.2.7 E-QUASIDIFFERENTIALS 74 2.3 OTHER DEFINITIONS OF GENERALIZED
GRADIENTS AND RELATIONS TO QUASIDIFFERENTIALS 75 2.3.1 SUBDIFFERENTIAL
IN THE SENSE OF CLARKE 75 2.3.2 QUASIDIFFERENTIAL AND PENOT
SUBDIFFERENTIAL AND SUPERDIFFERENTIAL 77 2.3.3 QUASIDIFFERENTIAL AND
CLARKE SUBDIFFERENTIAL 77 2.4 CODIFFERENTIABLE FUNCTIONS 78 2.4.1
DEFINITION AND EXAMPLES 78 2.4.2 CODIFFERENTIAL CALCULUS 79 2.4.3
CONTINUOUSLY CODIFFERENTIABLE SETS 80 2.4.4 TWICE CODIFFERENTIABLE
FUNCTIONS 81 2.5 OPTIMIZATION PROBLEMS AND OPTIMALITY CONDITIONS.
NECESSARY AND SUFFICIENT OPTIMALITY CONDITIONS 83 2.5.1 CHARACTERIZATION
OF MINIMA 83 2.6 UNCONSTRAINED MINIMIZATION 85 2.6.1 MINIMUM)OF A
QUASIDIFFERENTIABLE FUNCTION 85 2.6.2 MINIMUM OF A SUBDIFFERENTIABLE
FUNCTION 85 2.6.3 MINIMUM OF A HYPODIFFERENTIABLE FUNCTION 86 2.7
CONSTRAINED MINIMIZATION 86 . 2.7.1 MINIMUM OF A CONVEX FUNCTION ON A
CONVEX SET 86 2.7.2 MINIMUM OF A SUBDIFFERENTIABLE FUNCTION ON AN
ARBITRARY SET 86 2.7.3 MINIMUM OF A QUASIDIFFERENTIABLE FUNCTION ON A
QUASIDIFFERENTIABLE SET 88 2.7.4 MINIMUM OF A HYPODIFFERENTIABLE
FUNCTION ON A HYPODIFFERENTIABLE SET 89 2.7.5 EXACT PENALTY FUNCTIONS 90
REFERENCES OF CHAPTER 2 91 I 3. NONSMOOTH MECHANICS I. NONSMOOTH
MODELLING IN MECHANICS 93 3.1 ELEMENTS OF MECHANICS. CONVEX
SUPERPOTENTIALS 93 TABJE OF CONTENTS 3.2 NONCONVEX SUPERPOTENTIALS AND
NONCONVEX QUASIDIFFERENTIABLE (QD)-SUPERPOTENTIALS 102 3.3 BOUNDARY
CONDITIONS EXPRESSED VIA CONVEX SUPERPOTENTIALS 108 3.4 BOUNDARY
CONDITIONS AND INTERFACE LAWS EXPRESSED VIA NONCONVEX QD-SUPERPOTENTIALS
113 3.5 MATERIAL LAWS DERIVED BY CONVEX SUPERPOTENTIALS 122 3.5.1 CONVEX
SUPERPOTENTIALS 122 3.5.2 NONCONVEX QD-SUPERPOTENTIALS 127 3.6 TWO- AND
THREE DIMENSIONAL QD-SUPERPOTENTIAL LAWS .... 131 REFERENCES OF CHAPTER
3 135 4. NONSMOOTH MECHANICS II. VARIATIONAL FORMULATIONS USING
QUASIDIFFERENTIABILITY . 139 4.1 THE DERIVATION OF VARIATIONAL
FORMULATIONS FOR STATIC PROBLEMS INVOLVING QD-SUPERPOTENTIALS 139 4.2
ADHESIVE CONTACT PROBLEM IN ELASTIC BODIES 147 4.3 LAMINATED VON KARMAN
PLATES. DELAMINATION EFFECTS .... 153 4.4 A QD-SUPERPOTENTIAL APPROACH
TO THE SKIN FRICTION EFFECT IN PLANE ELASTICITY 160 4.4.1 THE CASE OF
LINEAR ELASTICITY 160 4.4.2 EXTENSION OF THE THEORY FOR THE CASE OF
FUZZY EFFECTS .. 164 4.5 ON THE COMBINATION OF Q-D-SUPERPOTENTIALS WITH
CONVEX SUPERPOTENTIALS. NONLINEAR ELASTICITY 166 4.6 Q.D-SUPERPOTENTIALS
IN SEMIPERMEABILITY PROBLEMS 171 REFERENCES OF CHAPTER 4 174 5.
ADDITIONAL TOPICS. STABILITY, ECONOMICS, FLOW PROBLEMS, DYNAMIC PROBLEMS
177 5.1 STABILITY OF STRUCTURES WITH QUASIDIFFERENTIAL BOUNDARY
CONDITIONS 177 5.1.1 THE NONLINEAR EIGENVALUE PROBLEM 177 5.1.2
FORMULATION OF NONCONVEX ENERGY MINIMIZATION PROBLEM 181 5.1.3 EXISTENCE
RESULT 182 5.1.4 APPLICATION IN A 3-D ELASTICITY PROBLEM 184 5.2
NONLINEAR, NONMONOTONE NETWORK FLOW PROBLEMS 187 VIII TABLE OF CONTENTS
5.2.1 FORMULATION OF THE PROBLEM 187 5.2.2~ MONOTONE SUBDIFFERENTIAL
NETWORK FLOW PROBLEMS 188 5.2.3 NONMONOTONE NETWORK FLOW PROBLEMS 189
5.3 RIGID VISCOPLASTIC FLOW PROBLEMS IN CYLINDRICAL PIPES WITH ADHESION
OR NONMONOTONE FRICTION 190 5.4 TIME-DEPENDENT Q)-SUPERPOTENTIALS AND
RELATED VARIATIONAL FORMULATIONS. VON KARMAN PLATES AND THERMOELASTICITY
194 5.4.1 DYNAMIC QI3-SUPERPOTENTIALS IN THE THEORY OF VON KARMAN PLATES
194 5.4.2 DYNAMIC QD-SUPERPOTENTIALS IN LINEAR THERMOELASTICITY 198
REFERENCES OF CHAPTER 5 202 6. NONSMOOTH OPTIMIZATION ALGORITHMS.
QUASIDIFFERENTIABLE AND CODIFFERENTIABLE OPTIMIZATION 205 6.1
HYPODIFFERENTIABLE OPTIMIZATION ALGORITHMS 205 6.1.1 THE METHOD OF
HYPODIFFERENTIAL DESCENT 205 6.1.2 FINDING THE DIRECTION OF
HYPODIFFERENTIAL DESCENT 212 6.1.3 ON THE MINIMIZATION OF THE DIFFERENCE
OF THE MAXIMUMLOF SMOOTH FUNCTIONS 215 6.1.4 CODIFFERENTIAL OPTIMIZATION
ALGORITHMS 222 6.2 OPTIMIZATION OF DIFFERENCE CONVEX (D.C.) FUNCTIONS
224 6.2.1 THE RELAXATION METHOD FOR MINIMIZING D.C. FUNCTIONS 230 6.3
EXACT PENALTY QUASIDIFFERENTIABLE FUNCTIONS 236 6.3.1 CONVEX CASE 246
6.3.2 THE NONLINEAR PROGRAMMING PROBLEM 251 REFERENCES OF CHAPTER 6 252
7. NONSMOOTH COMPUTATIONAL MECHANICS I. MODELLING AND APPLICATIONS 253
7.1 QUASIDIFFERENTIAL ENERGY OPTIMIZATION IN MECHANICS 253 I 7.1.1
SMOOTH UNCONSTRAINED CASE 255 7.1.2 SUBDIFFERENTIABLE UNCONSTRAINED CASE
256 7.1.3 QUASIDIFFERENTIABLE UNCONSTRAINED CASE 256 7.1.4 DIFFERENCE
CONVEX (D.C.) UNCONSTRAINED CASE 257 7.1.5 INEQUALITY CONSTRAINED
PROBLEMS 258 TABIE OF CONTENTS IX 7.2 STRUCTURAL ANALYSIS APPLICATIONS
259 7.2.1 A MODEL PROBLEM FOR DISCRETE STRUCTURES WITH INTERFACES 260
7.2.2 LINEAR ELASTIC STRUCTURE WITH SUBDIFFERENTIAL INTERFACE LAWS AND
BOUNDARY CONDITIONS 263 7.2.3 SUBDIFFERENTIAL MATERIAL LAWS AND
SUBDIFFERENTIAL INTERFACE OR BOUNDARY CONDITIONS 268 7.2.4 LINEAR
ELASTIC STRUCTURES WITH QUASIDIFFERENTIAL INTERFACE LAWS OR BOUNDARY
CONDITIONS 269 7.3 NONCONVEX ELASTOPLASTICITY 276 7.3.1 HOLONOMIC,
HENCKY-TYPE ELASTOPLASTICITY 278 7.3.2 CONVEX ANALYSIS AND RATE
ELASTOPLASTICITY 283 7.3.3 NONCONVEX ANALYSIS AND ELASTOPLASTICITY 286
REFERENCES OF CHAPTER 7 293 8. NONSMOOTH COMPUTATIONAL MECHANICS II.
ALGORITHMS AND EXAMPLES 297 8.1 NONSMOOTH COMPUTATIONAL MECHANICS
ALGORITHMS 297 8.1.1 NUMERICAL OPTIMIZATION AND NONLINEAR COMPUTATIONAL
MECHANICS 298 8.1.2 CONVEX, NONSMOOTH OPTIMIZATION IN COMPUTATIONAL
MECHANICS 300 .8.1.3 NONCONVEX, NONSMOOTH OPTIMIZATION IN COMPUTATIONAL
MECHANICS 304 8.1.4 INCREMENTAL AND PATH-FOLLOWING METHODS 307 8.2
NUMERICAL EXAMPLES 311 8.2.1 MATERIAL INCLUSION PROBLEM IN COMPOSITES
311 8.2.2 ELASTIC, FRICTIONLESS AND FRICTIONAL STAMP PROBLEM 316 8.2.3
SHORT CANTILEVER RESTING ON A UNILATERAL SUPPORT 320 8.2.4 DELAMINATION
EFFECTS IN LAYERED COMPOSITE BEAMS .... 332 8.2.5 NONMONOTONE SKIN
EFFECTS IN ADHESIVE JOINTS 338 REFERENCES OF CHAPTER 8 342 SUBJECT INDEX
.-, 345
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| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV011106953 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:04:06Z |
| institution | BVB |
| isbn | 0792340930 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007441863 |
| oclc_num | 34675805 |
| open_access_boolean | |
| owner | DE-91 DE-BY-TUM DE-29T DE-703 DE-634 |
| owner_facet | DE-91 DE-BY-TUM DE-29T DE-703 DE-634 |
| physical | XVII, 348 S. graph. Darst. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Kluwer |
| record_format | marc |
| series | Nonconvex optimization and its applications |
| series2 | Nonconvex optimization and its applications |
| spelling | Quasidifferentiability and nonsmooth modelling in mechanics, engineering and economics Vladimir F. Dem'yanov ... Dordrecht [u.a.] Kluwer 1996 XVII, 348 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Nonconvex optimization and its applications 10 Ingénierie - Modèles mathématiques ram Mécanique appliquée - Modèles mathématiques ram Optimisation mathématique ram fonction quasidifférentiable inriac ingéniérie inriac modélisation inriac mécanique inriac optimisation non lissée inriac Économie politique - Modèles mathématiques ram économie inriac Ingenieurwissenschaften Mathematisches Modell Wirtschaft Economics Mathematical models Engineering Mathematical models Mechanics, Applied Mathematical models Nonsmooth optimization Quasidifferential calculus Anwendung (DE-588)4196864-5 gnd rswk-swf Nichtglatte Mechanik (DE-588)4201235-1 gnd rswk-swf Quasidifferenzierbare Funktion (DE-588)4176636-2 gnd rswk-swf Nichtglatte Optimierung (DE-588)4120798-1 gnd rswk-swf Quasidifferenzierbare Funktion (DE-588)4176636-2 s Anwendung (DE-588)4196864-5 s DE-604 Nichtglatte Optimierung (DE-588)4120798-1 s Nichtglatte Mechanik (DE-588)4201235-1 s Demʹjanov, Vladimir F. 1938- Sonstige (DE-588)108348482 oth Nonconvex optimization and its applications 10 (DE-604)BV010085908 10 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007441863&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Quasidifferentiability and nonsmooth modelling in mechanics, engineering and economics Nonconvex optimization and its applications Ingénierie - Modèles mathématiques ram Mécanique appliquée - Modèles mathématiques ram Optimisation mathématique ram fonction quasidifférentiable inriac ingéniérie inriac modélisation inriac mécanique inriac optimisation non lissée inriac Économie politique - Modèles mathématiques ram économie inriac Ingenieurwissenschaften Mathematisches Modell Wirtschaft Economics Mathematical models Engineering Mathematical models Mechanics, Applied Mathematical models Nonsmooth optimization Quasidifferential calculus Anwendung (DE-588)4196864-5 gnd Nichtglatte Mechanik (DE-588)4201235-1 gnd Quasidifferenzierbare Funktion (DE-588)4176636-2 gnd Nichtglatte Optimierung (DE-588)4120798-1 gnd |
| subject_GND | (DE-588)4196864-5 (DE-588)4201235-1 (DE-588)4176636-2 (DE-588)4120798-1 |
| title | Quasidifferentiability and nonsmooth modelling in mechanics, engineering and economics |
| title_auth | Quasidifferentiability and nonsmooth modelling in mechanics, engineering and economics |
| title_exact_search | Quasidifferentiability and nonsmooth modelling in mechanics, engineering and economics |
| title_full | Quasidifferentiability and nonsmooth modelling in mechanics, engineering and economics Vladimir F. Dem'yanov ... |
| title_fullStr | Quasidifferentiability and nonsmooth modelling in mechanics, engineering and economics Vladimir F. Dem'yanov ... |
| title_full_unstemmed | Quasidifferentiability and nonsmooth modelling in mechanics, engineering and economics Vladimir F. Dem'yanov ... |
| title_short | Quasidifferentiability and nonsmooth modelling in mechanics, engineering and economics |
| title_sort | quasidifferentiability and nonsmooth modelling in mechanics engineering and economics |
| topic | Ingénierie - Modèles mathématiques ram Mécanique appliquée - Modèles mathématiques ram Optimisation mathématique ram fonction quasidifférentiable inriac ingéniérie inriac modélisation inriac mécanique inriac optimisation non lissée inriac Économie politique - Modèles mathématiques ram économie inriac Ingenieurwissenschaften Mathematisches Modell Wirtschaft Economics Mathematical models Engineering Mathematical models Mechanics, Applied Mathematical models Nonsmooth optimization Quasidifferential calculus Anwendung (DE-588)4196864-5 gnd Nichtglatte Mechanik (DE-588)4201235-1 gnd Quasidifferenzierbare Funktion (DE-588)4176636-2 gnd Nichtglatte Optimierung (DE-588)4120798-1 gnd |
| topic_facet | Ingénierie - Modèles mathématiques Mécanique appliquée - Modèles mathématiques Optimisation mathématique fonction quasidifférentiable ingéniérie modélisation mécanique optimisation non lissée Économie politique - Modèles mathématiques économie Ingenieurwissenschaften Mathematisches Modell Wirtschaft Economics Mathematical models Engineering Mathematical models Mechanics, Applied Mathematical models Nonsmooth optimization Quasidifferential calculus Anwendung Nichtglatte Mechanik Quasidifferenzierbare Funktion Nichtglatte Optimierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007441863&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV010085908 |
| work_keys_str_mv | AT demʹjanovvladimirf quasidifferentiabilityandnonsmoothmodellinginmechanicsengineeringandeconomics |