Introduction to piecewise differentiable equations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
Karlsruhe
Inst. für Statistik und Math. Wirtschaftstheorie
1994
|
| Series: | Institut für Statistik und Mathematische Wirtschaftstheorie <Karlsruhe>: Preprint series
53 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Zugl.: Karlsruhe, Univ., Habil.-Schr., 1995 |
| Physical Description: | 130 S. |
Staff View
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| 245 | 1 | 0 | |a Introduction to piecewise differentiable equations |c Stefan Scholtes. [Universität Karlsruhe, Institut für Statistik und Mathematische Wirtschaftstheorie an der Universität Fridericiana Karlsruhe] |
| 264 | 1 | |a Karlsruhe |b Inst. für Statistik und Math. Wirtschaftstheorie |c 1994 | |
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| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Institut für Statistik und Mathematische Wirtschaftstheorie <Karlsruhe>: Preprint series |v 53 | |
| 500 | |a Zugl.: Karlsruhe, Univ., Habil.-Schr., 1995 | ||
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Record in the Search Index
| _version_ | 1808137644157173760 |
|---|---|
| adam_text |
CONTENTS
1
SAMPLE
PROBLEMS
FOR
NONSMOOTH
EQUATIONS
3
1.1
COMPLEMENTARITY
PROBLEMS
.
5
1.1.1
EQUILIBRIA
OF
DYNAMICAL
SYSTEMS
.
5
1.1.2
NONLINEAR
COMPLEMENTARITY
PROBLEMS
.
7
1.1.3
COMMENTS
AND
REFERENCES
.
8
1.2
STATIONARY
SOLUTIONS
OF
PARAMETRIC
PROGRAMS
.
8
1.2.1
MULTIOBJECTIVE
OPTIMIZATION
.
8
1.2.2
THE
KOJIMA
MAPPING
.
10
1.2.3
COMMENTS
AND
REFERENCES
.
11
A.L
DIFFERENTIABILITY
VERSUS
NONDIFFERENTIABILITY
.
11
2
PIECEWISE
AFFINE
FUNCTIONS
15
2.1
ELEMENTS
FROM
POLYHEDRAL
THEORY
.
15
2.1.1
CONVEX
SETS
AND
CONVEX
CONES
.
16
2.1.2
POLYHEDRAL
SETS
AND
POLYHEDRAL
CONES
.
17
2.1.3
THE
FACE
LATTICE
OF
A
POLYHEDRON
.
19
2.1.4
COMMENTS
AND
REFERENCES
.
21
2.2
BASIC
NOTIONS
AND
PROPERTIES
.
22
2.2.1
REPRESENTATIONS
OF
PIECEWISE
AFFINE
FUNCTIONS
.
23
2.2.2
LOCAL
APPROXIMATIONS
OF
PIECEWISE
AFFINE
FUNCTIONS
.
28
2.2.3
LIPSCHITZ
CONTINUITY
OF
PIECEWISE
AFFINE
FUNCTIONS
.
30
2.2.4
COMMENTS
AND
REFERENCES
.
31
2.3
PIECEWISE
AFFINE
HOMEOMORPHISMS
.
31
2.3.1
COHERENTLY
ORIENTED
PIECEWISE
AFFINE
FUNCTIONS
.
32
2.3.2
PIECEWISE
AFFINE
LOCAL
HOMEOMORPHISMS
.
40
2.3.3
THE
FACTORIZATION
LEMMA
.
45
2.3.4
THE
BRANCHING
NUMBER
THEOREM
.
48
2.3.5
COMMENTS
AND
REFERENCES
.
51
2.4
EUCLIDEAN
PROJECTIONS
.
52
2.4.1
THE
EUCLIDEAN
PROJECTION
ONTO
A
POLYHEDRON
.
54
2.4.2
THE
NORMAL
MANIFOLD
.
55
2.4.3
AN
APPLICATION:
AFFINE
VARIATIONAL
INEQUALITIES
.
59
2.4.4
COMMENTS
AND
REFERENCES
.
60
A.
2
THE
RECESSION
FUNCTION
.
61
2
CONTENTS
3
ELEMENTS
FROM
NONSMOOTH
ANALYSIS
65
3.1
THE
BOULIGAND
DERIVATIVE
.
65
3.1.1
THE
B-DERIVATIVE
OF
A
LOCALLY
LIPSCHITZ
CONTINUOUS
FUNCTION
.
69
3.1.2
STRONGLY
B-DIFFERENTIABLE
FUNCTIONS
.
72
3.1.3
COMMENTS
AND
REFERENCES
.
74
3.2
INVERSE
AND
IMPLICIT
FUNCTION
THEOREMS
.
75
3.2.1
B-DERIVATIVES
OF
LOCAL
LIPSCHITZ
HOMEOMORPHISMS
.
81
3.2.2
AN
INVERSE
FUNCTION
THEOREM
.
84
3.2.3
HADAMARD
'
S
THEOREM
.
85
3.2.4
COMMENTS
AND
REFERENCES
.
87
A.
3
THE
INVERSE
FUNCTION
THEOREMS
OF
CLARKE
AND
KUMMER
.
87
4
PIECEWISE
DIFFERENTIABLE
FUNCTIONS
91
4.1
BASIC
NOTIONS
AND
PROPERTIES
.
91
4.1.1
LOCAL
LIPSCHITZ
CONTINUITY
.
93
4.1.2
B-DIFFERENTIABILITY
.
95
4.1.3
STRONG
B-DIFFERENTIABILITY
.
98
4.1.4
CONTINUOUS
DIFFERENTIABILITY
.
100
4.1.5
COMMENTS
AND
REFERENCES
.
101
4.2
PIECEWISE
DIFFERENTIABLE
HOMEOMORPHISMS
.
101
4.2.1
AN
IMPLICIT
FUNCTION
THEOREM
.
103
4.2.2
A
BOUND
FOR
THE
CONDITION
NUMBEI
.
107
4.2.3
COMMENTS
AND
REFERENCES
.
109
A.
4
A
FORMULA
FOR
THE
GENERALIZED
JACOBIAN
.
109
5
APPLICATIONS
111
5.1
VARIATIONAL
INEQUALITIES
AND
NORMAL
MAPS
.
ILL
5.1.1
A
HOMEOMORPHISM
CONDITION
FOR
NORMAL
MAPS
OF
POLYHEDRA
.
112
5.1.2
COMMENTS
AND
REFERENCES
.
114
5.2
SENSITIVITY
ANALYSIS
FOR
MATHEMATICAL
PROGRAMS
.
114
5.2.1
SENSITIVITY
ANALYSIS
OF
STATIONARY
SOLUTIONS
.
115
5.2.2
SENSITIVITY
ANALYSIS
OF
LOCAL
MINIMIZERS
.
120
5.2.3
COMMENTS
AND
REFERENCES
.
122
A.
5.2
THE
F-DERIVATIVES
OF
THE
SELECTION
FUNCTIONS
.
122 |
| any_adam_object | 1 |
| author | Scholtes, Stefan 1960- |
| author_GND | (DE-588)170951510 |
| author_facet | Scholtes, Stefan 1960- |
| author_role | aut |
| author_sort | Scholtes, Stefan 1960- |
| author_variant | s s ss |
| building | Verbundindex |
| bvnumber | BV010635380 |
| classification_rvk | SK 490 |
| ctrlnum | (OCoLC)75706021 (DE-599)BVBBV010635380 |
| discipline | Mathematik |
| format | Book |
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| genre_facet | Hochschulschrift |
| id | DE-604.BV010635380 |
| illustrated | Not Illustrated |
| indexdate | 2024-08-23T00:53:51Z |
| institution | BVB |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007095188 |
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| physical | 130 S. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Inst. für Statistik und Math. Wirtschaftstheorie |
| record_format | marc |
| series | Institut für Statistik und Mathematische Wirtschaftstheorie <Karlsruhe>: Preprint series |
| series2 | Institut für Statistik und Mathematische Wirtschaftstheorie <Karlsruhe>: Preprint series |
| spelling | Scholtes, Stefan 1960- Verfasser (DE-588)170951510 aut Introduction to piecewise differentiable equations Stefan Scholtes. [Universität Karlsruhe, Institut für Statistik und Mathematische Wirtschaftstheorie an der Universität Fridericiana Karlsruhe] Karlsruhe Inst. für Statistik und Math. Wirtschaftstheorie 1994 130 S. txt rdacontent n rdamedia nc rdacarrier Institut für Statistik und Mathematische Wirtschaftstheorie <Karlsruhe>: Preprint series 53 Zugl.: Karlsruhe, Univ., Habil.-Schr., 1995 Infinitesimalrechnung (DE-588)4072798-1 gnd rswk-swf Differenzierbarkeit (DE-588)4149807-0 gnd rswk-swf Nichtglatte Analysis (DE-588)4379207-8 gnd rswk-swf Variationsrechnung (DE-588)4062355-5 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Nichtglatte Analysis (DE-588)4379207-8 s Differenzierbarkeit (DE-588)4149807-0 s DE-604 Infinitesimalrechnung (DE-588)4072798-1 s Variationsrechnung (DE-588)4062355-5 s 1\p DE-604 Institut für Statistik und Mathematische Wirtschaftstheorie <Karlsruhe>: Preprint series 53 (DE-604)BV012346399 53 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007095188&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 | Scholtes, Stefan 1960- Introduction to piecewise differentiable equations Institut für Statistik und Mathematische Wirtschaftstheorie <Karlsruhe>: Preprint series Infinitesimalrechnung (DE-588)4072798-1 gnd Differenzierbarkeit (DE-588)4149807-0 gnd Nichtglatte Analysis (DE-588)4379207-8 gnd Variationsrechnung (DE-588)4062355-5 gnd |
| subject_GND | (DE-588)4072798-1 (DE-588)4149807-0 (DE-588)4379207-8 (DE-588)4062355-5 (DE-588)4113937-9 |
| title | Introduction to piecewise differentiable equations |
| title_auth | Introduction to piecewise differentiable equations |
| title_exact_search | Introduction to piecewise differentiable equations |
| title_full | Introduction to piecewise differentiable equations Stefan Scholtes. [Universität Karlsruhe, Institut für Statistik und Mathematische Wirtschaftstheorie an der Universität Fridericiana Karlsruhe] |
| title_fullStr | Introduction to piecewise differentiable equations Stefan Scholtes. [Universität Karlsruhe, Institut für Statistik und Mathematische Wirtschaftstheorie an der Universität Fridericiana Karlsruhe] |
| title_full_unstemmed | Introduction to piecewise differentiable equations Stefan Scholtes. [Universität Karlsruhe, Institut für Statistik und Mathematische Wirtschaftstheorie an der Universität Fridericiana Karlsruhe] |
| title_short | Introduction to piecewise differentiable equations |
| title_sort | introduction to piecewise differentiable equations |
| topic | Infinitesimalrechnung (DE-588)4072798-1 gnd Differenzierbarkeit (DE-588)4149807-0 gnd Nichtglatte Analysis (DE-588)4379207-8 gnd Variationsrechnung (DE-588)4062355-5 gnd |
| topic_facet | Infinitesimalrechnung Differenzierbarkeit Nichtglatte Analysis Variationsrechnung Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007095188&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV012346399 |
| work_keys_str_mv | AT scholtesstefan introductiontopiecewisedifferentiableequations |