Perturbation analysis of optimization problems:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
2000
|
| Series: | Springer series in operations research
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XVIII, 601 S. |
| ISBN: | 0387987053 9780387987057 9781461271291 |
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MARC
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| 020 | |a 9780387987057 |9 978-0-387-98705-7 | ||
| 020 | |a 9781461271291 |c pbk. |9 978-1-4612-7129-1 | ||
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| 100 | 1 | |a Bonnans, J. Frédéric |d 1957- |e Verfasser |0 (DE-588)122195507 |4 aut | |
| 245 | 1 | 0 | |a Perturbation analysis of optimization problems |c J. Frédéric Bonnans ; Alexander Shapiro |
| 264 | 1 | |a New York [u.a.] |b Springer |c 2000 | |
| 300 | |a XVIII, 601 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Springer series in operations research | |
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 650 | 7 | |a Operations research |2 gtt | |
| 650 | 7 | |a Optimaliseren |2 gtt | |
| 650 | 4 | |a Optimisation mathématique | |
| 650 | 4 | |a Perturbation (Mathématiques) | |
| 650 | 7 | |a Programação matemática |2 larpcal | |
| 650 | 7 | |a Programação não linear |2 larpcal | |
| 650 | 4 | |a Mathematical optimization | |
| 650 | 4 | |a Perturbation (Mathematics) | |
| 650 | 0 | 7 | |a Störungstheorie |0 (DE-588)4128420-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Optimierung |0 (DE-588)4043664-0 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Störungstheorie |0 (DE-588)4128420-3 |D s |
| 689 | 0 | 1 | |a Optimierung |0 (DE-588)4043664-0 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Shapiro, Alexander |d 1949- |e Verfasser |0 (DE-588)130425850 |4 aut | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-1-4612-1394-9 |
| 856 | 4 | 2 | |m DNB Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009017107&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-009017107 | |
Record in the Search Index
| _version_ | 1807500728339529728 |
|---|---|
| adam_text |
CONTENTS
BASIC
NOTATION
XIII
1
INTRODUCTION
1
2
BACKGROUND
MATERIAL
8
2.1
BASIC
FUNCTIONAL
ANALYSIS
.
8
2.1.1
TOPOLOGICAL
VECTOR
SPACES
.
8
2.1.2
THE
HAHN-BANACH
THEOREM
.
17
2.1.3
BANACH
SPACES
.
21
2.1.4
CONES,
DUALITY
AND
RECESSION
CONES
.
31
2.2
DIRECTIONAL
DIFFERENTIABILITY
AND
TANGENT
CONES
.
34
2.2.1
FIRST
ORDER
DIRECTIONAL
DERIVATIVES
.
34
2.2.2
SECOND
ORDER
DERIVATIVES
.
37
2.2.3
DIRECTIONAL
EPIDERIVATIVES
OF
EXTENDED
REAL
VALUED
FUNCTIONS
.
39
2.2.4
TANGENT
CONES
.
44
2.3
ELEMENTS
OF
MULTIFUNCTIONS
THEORY
.
54
2.3.1
THE
GENERALIZED
OPEN
MAPPING
THEOREM
.
55
2.3.2
OPENNESS,
STABILITY
AND
METRIC
REGULARITY
.
57
2.3.3
STABILITY
OF
NONLINEAR
CONSTRAINED
SYSTEMS
.
60
2.3.4
CONSTRAINT
QUALIFICATION
CONDITIONS
.
67
2.3.5
CONVEX
MAPPINGS
.
72
2.4
CONVEX
FUNCTIONS
.
74
2.4.1
CONTINUITY
.
74
VIII
CONTENTS
2.4.2
CONJUGACY
.
77
2.4.3
SUBDIFFERENTIABILITY
.
81
2.4.4
CHAIN
RULES
.
92
2.5
DUALITY
THEORY
.
95
2.5.1
CONJUGATE
DUALITY
.
95
2.5.2
LAGRANGIAN
DUALITY
.
104
2.5.3
EXAMPLES
AND
APPLICATIONS
OF
DUALITY
SCHEMES
.
.
.
107
2.5.4
APPLICATIONS
TO
SUBDIFFERENTIAL
CALCULUS
.
113
2.5.5
MINIMIZATION
OF
A
MAXIMUM
OVER
A
COMPACT
SET
.
.
117
2.5.6
CONIC
LINEAR
PROBLEMS
.
125
2.5.7
GENERALIZED
LINEAR
PROGRAMMING
AND
POLYHEDRAL
MULTI
FUNCTIONS
.
133
3
OPTIMALITY
CONDITIONS
146
3.1
FIRST
ORDER
OPTIMALITY
CONDITIONS
.
147
3.1.1
LAGRANGE
MULTIPLIERS
.
147
3.1.2
GENERALIZED
LAGRANGE
MULTIPLIERS
.
153
3.1.3
EKELAND
'
S
VARIATIONAL
PRINCIPLE
.
156
3.1.4
FIRST
ORDER
SUFFICIENT
CONDITIONS
.
159
3.2
SECOND
ORDER
NECESSARY
CONDITIONS
.
162
3.2.1
SECOND
ORDER
TANGENT
SETS
.
162
3.2.2
GENERAL
FORM
OF
SECOND
ORDER
NECESSARY
CONDITIONS
173
3.2.3
EXTENDED
POLYHEDRICITY
.
180
3.3
SECOND
ORDER
SUFFICIENT
CONDITIONS
.
186
3.3.1
GENERAL
FORM
OF
SECOND
ORDER
SUFFICIENT
CONDITIONS
186
3.3.2 QUADRATIC
AND
EXTENDED
LEGENDRE
FORMS
.
193
3.3.3
SECOND
ORDER
REGULARITY
OF
SETS
AND
"
NO
GAP
"
SECOND
ORDER
OPTIMALITY
CONDITIONS
.
198
3.3.4
SECOND
ORDER
REGULARITY
OF
FUNCTIONS
.
208
3.3.5
SECOND
ORDER
SUBDERIVATIVES
.
212
3.4
SPECIFIC
STRUCTURES
.
217
3.4.1
COMPOSITE
OPTIMIZATION
.
217
3.4.2
EXACT
PENALTY
FUNCTIONS
AND
AUGMENTED
DUALITY
.
.
222
3.4.3
LINEAR
CONSTRAINTS
AND
QUADRATIC
PROGRAMMING
.
.
.
228
3.4.4
A
REDUCTION
APPROACH
.
240
3.5
NONISOLATED
MINIMA
.
245
3.5.1
NECESSARY
CONDITIONS
FOR
QUADRATIC
GROWTH
.
245
3.5.2
SUFFICIENT
CONDITIONS
.
249
3.5.3
SUFFICIENT
CONDITIONS
BASED
ON
GENERAL
CRITICAL
DIREC
TIONS
.
256
4
STABILITY
AND
SENSITIVITY
ANALYSIS
260
4.1
STABILITY
OF
THE
OPTIMAL
VALUE
AND
OPTIMAL
SOLUTIONS
.
261
4.2
DIRECTIONAL
REGULARITY
.
266
CONTENTS
IX
4.3
FIRST
ORDER
DIFFERENTIABILITY
ANALYSIS
OF
THE
OPTIMAL
VALUE
FUNCTION
.
271
4.3.1
THE
CASE
OF
FIXED
FEASIBLE
SET
.
272
4.3.2
DIRECTIONAL
DIFFERENTIABILITY
OF
THE
OPTIMAL
VALUE
FUNC
TION
UNDER
ABSTRACT
CONSTRAINTS
.
278
4.4
QUANTITATIVE
STABILITY
OF
OPTIMAL
SOLUTIONS
AND
LAGRANGE
MULTI
PLIERS
.
286
4.4.1
LIPSCHITZIAN
STABILITY
IN
THE
CASE
OF
A
FIXED
FEASIBLE
SET
287
4.4.2
HOLDER
STABILITY
UNDER
ABSTRACT
CONSTRAINTS
.
290
4.4.3
QUANTITATIVE
STABILITY
OF
LAGRANGE
MULTIPLIERS
.
294
4.4.4
LIPSCHITZIAN
STABILITY
OF
OPTIMAL
SOLUTIONS
AND
LAGRANGE
MULTIPLIERS
.
299
4.5
DIRECTIONAL
STABILITY
OF
OPTIMAL
SOLUTIONS
.
303
4.5.1
HOLDER
DIRECTIONAL
STABILITY
.
303
4.5.2
LIPSCHITZIAN
DIRECTIONAL
STABILITY
.
305
4.6
QUANTITATIVE
STABILITY
ANALYSIS
BY
A
REDUCTION
APPROACH
.
.
314
4.6.1
NONDEGENERACY
AND
STRICT
COMPLEMENTARITY
.
315
4.6.2
STABILITY
ANALYSIS
.
320
4.7
SECOND
ORDER
ANALYSIS
IN
LIPSCHITZ
STABLE
CASES
.
323
4.7.1
UPPER
SECOND
ORDER
ESTIMATES
OF
THE
OPTIMAL
VALUE
FUNCTION
.
324
4.7.2
LOWER
ESTIMATES
WITHOUT
THE
SIGMA
TERM
.
332
4.7.3
THE
SECOND
ORDER
REGULAR
CASE
.
337
4.7.4
COMPOSITE
OPTIMIZATION
PROBLEMS
.
341
4.8
SECOND
ORDER
ANALYSIS
IN
HOLDER
STABLE
CASES
.
347
4.8.1
UPPER
SECOND
ORDER
ESTIMATES
OF
THE
OPTIMAL
VALUE
FUNCTION
.
347
4.8.2
LOWER
ESTIMATES
AND
EXPANSIONS
OF
OPTIMAL
SOLUTIONS
355
4.8.3
EMPTY
SETS
OF
LAGRANGE
MULTIPLIERS
.
357
4.8.4
HOLDER
EXPANSIONS
FOR
SECOND
ORDER
REGULAR
PROBLEMS
363
4.9
ADDITIONAL
RESULTS
.
365
4.9.1
EQUALITY
CONSTRAINED
PROBLEMS
.
365
4.9.2
UNIFORM
APPROXIMATIONS
OF
THE
OPTIMAL
VALUE
AND
OPTIMAL
SOLUTIONS
.
369
4.9.3
SECOND
ORDER
ANALYSIS
FOR
NONISOLATED
OPTIMA
.
.
.
379
4.10
SECOND
ORDER
ANALYSIS
IN
FUNCTIONAL
SPACES
.
386
4.10.1
SECOND
ORDER
TANGENT
SETS
IN
FUNCTIONAL
SPACES
OF
CONTINUOUS
FUNCTIONS
.
386
4.10.2
SECOND
ORDER
DERIVATIVES
OF
OPTIMAL
VALUE
FUNCTIONS
391
4.10.3
SECOND
ORDER
EXPANSIONS
IN
FUNCTIONAL
SPACES
.
.
.
394
5
ADDITIONAL
MATERIAL
AND
APPLICATIONS
401
5.1
VARIATIONAL
INEQUALITIES
.
401
5.1.1
STANDARD
VARIATIONAL
INEQUALITIES
.
-.
.
402
5.1.2
GENERALIZED
EQUATIONS
.
407
X.
CONTENTS
5.1.3
STRONG
REGULARITY
.
412
5.1.4
STRONG
REGULARITY
AND
SECOND
ORDER
OPTIMALITY
CONDI
TIONS
.
422
5.1.5
STRONG
STABILITY
.
427
5.1.6
SOME
EXAMPLES
AND
APPLICATIONS
.
429
5.2
NONLINEAR
PROGRAMMING
.
436
5.2.1
FINITE
DIMENSIONAL
LINEAR
PROGRAMS
.
436
5.2.2
OPTIMALITY
CONDITIONS
FOR
NONLINEAR
PROGRAMS
.
.
.
440
5.2.3
LIPSCHITZ
EXPANSIONS
OF
OPTIMAL
SOLUTIONS
.
445
5.2.4
HOLDER
EXPANSION
OF
OPTIMAL
SOLUTIONS
.
453
5.2.5
HIGH
ORDER
EXPANSIONS
OF
OPTIMAL
SOLUTIONS
AND
LA
GRANGE
MULTIPLIERS
.
459
5.2.6
ELECTRICAL
NETWORKS
.
462
5.2.7
THE
CHAIN
PROBLEM
.
465
5.3
SEMI-DEFINITE
PROGRAMMING
.
470
5.3.1
GEOMETRY
OF
THE
CONES
OF
NEGATIVE
SEMIDEFINITE
MATRI
CES
.
472
5.3.2
MATRIX
CONVEXITY
.
477
5.3.3
DUALITY
.
479
5.3.4
FIRST
ORDER
OPTIMALITY
CONDITIONS
.
483
5.3.5
SECOND
ORDER
OPTIMALITY
CONDITIONS
.
486
5.3.6
STABILITY
AND
SENSITIVITY
ANALYSIS
.
491
5.4
SEMI-INFINITE
PROGRAMMING
.
496
5.4.1
DUALITY
.
497
5.4.2
FIRST
ORDER
OPTIMALITY
CONDITIONS
.
506
5.4.3
SECOND
ORDER
OPTIMALITY
CONDITIONS
.
515
5.4.4
PERTURBATION
ANALYSIS
.
521
6
OPTIMAL
CONTROL
527
6.1
INTRODUCTION
.
527
6.2
LINEAR
AND
SEMILINEAR
ELLIPTIC
EQUATIONS
.
528
6.2.1
THE
DIRICHLET
PROBLEM
.
528
6.2.2
SEMILINEAR
ELLIPTIC
EQUATIONS
.
534
6.2.3
STRONG
SOLUTIONS
.
537
6.3
OPTIMAL
CONTROL
OF
A
SEMILINEAR
ELLIPTIC
EQUATION
.
539
6.3.1
EXISTENCE
OF
SOLUTIONS,
FIRST
ORDER
OPTIMALITY
SYSTEM
539
6.3.2
SECOND
ORDER
NECESSARY
OR
SUFFICIENT
CONDITIONS
.
.
543
6.3.3
SOME
SPECIFIC
CONTROL
CONSTRAINTS
.
548
6.3.4
SENSITIVITY
ANALYSIS
.
550
6.3.5
STATE
CONSTRAINED
OPTIMAL
CONTROL
PROBLEM
.
553
6.3.6
OPTIMAL
CONTROL
OF
AN
ILL-POSED
SYSTEM
.
555
6.4
THE
OBSTACLE
PROBLEM
.
558
6.4.1
PRESENTATION
OF
THE
PROBLEM
.
558
6.4.2
POLYHEDRICITY
.
559
6.4.3
BASIC
CAPACITY
THEORY
.
560
CONTENTS
XI
6.4.4
SENSITIVITY
ANALYSIS
AND
OPTIMAL
CONTROL
.
566
7
BIBLIOGRAPHICAL
NOTES
570
7.1
BACKGROUND
MATERIAL
.
570
7.2
OPTIMALITY
CONDITIONS
.
572
7.3
STABILITY
AND
SENSITIVITY
ANALYSIS
.
574
7.4
APPLICATIONS
.
578
7.4.1
VARIATIONAL
INEQUALITIES
.
578
7.4.2
NONLINEAR
PROGRAMMING
.
580
7.4.3
SEMI-DEFINITE
PROGRAMMING
.
580
7.4.4
SEMI-INFINITE
PROGRAMMING
.
581
7.5
OPTIMAL
CONTROL
.
581
REFERENCES
583
INDEX
595 |
| any_adam_object | 1 |
| author | Bonnans, J. Frédéric 1957- Shapiro, Alexander 1949- |
| author_GND | (DE-588)122195507 (DE-588)130425850 |
| author_facet | Bonnans, J. Frédéric 1957- Shapiro, Alexander 1949- |
| author_role | aut aut |
| author_sort | Bonnans, J. Frédéric 1957- |
| author_variant | j f b jf jfb a s as |
| building | Verbundindex |
| bvnumber | BV013230366 |
| callnumber-first | Q - Science |
| callnumber-label | QA871 |
| callnumber-raw | QA871 |
| callnumber-search | QA871 |
| callnumber-sort | QA 3871 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 870 SK 880 |
| classification_tum | MAT 910f MAT 418f |
| ctrlnum | (OCoLC)43311747 (DE-599)BVBBV013230366 |
| dewey-full | 519.3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.3 |
| dewey-search | 519.3 |
| dewey-sort | 3519.3 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV013230366 |
| illustrated | Not Illustrated |
| indexdate | 2024-08-16T00:10:20Z |
| institution | BVB |
| isbn | 0387987053 9780387987057 9781461271291 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009017107 |
| oclc_num | 43311747 |
| open_access_boolean | |
| owner | DE-29T DE-20 DE-355 DE-BY-UBR DE-703 DE-91G DE-BY-TUM DE-384 DE-706 DE-634 DE-83 DE-11 DE-188 |
| owner_facet | DE-29T DE-20 DE-355 DE-BY-UBR DE-703 DE-91G DE-BY-TUM DE-384 DE-706 DE-634 DE-83 DE-11 DE-188 |
| physical | XVIII, 601 S. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer series in operations research |
| spelling | Bonnans, J. Frédéric 1957- Verfasser (DE-588)122195507 aut Perturbation analysis of optimization problems J. Frédéric Bonnans ; Alexander Shapiro New York [u.a.] Springer 2000 XVIII, 601 S. txt rdacontent n rdamedia nc rdacarrier Springer series in operations research Hier auch später erschienene, unveränderte Nachdrucke Operations research gtt Optimaliseren gtt Optimisation mathématique Perturbation (Mathématiques) Programação matemática larpcal Programação não linear larpcal Mathematical optimization Perturbation (Mathematics) Störungstheorie (DE-588)4128420-3 gnd rswk-swf Optimierung (DE-588)4043664-0 gnd rswk-swf Störungstheorie (DE-588)4128420-3 s Optimierung (DE-588)4043664-0 s DE-604 Shapiro, Alexander 1949- Verfasser (DE-588)130425850 aut Erscheint auch als Online-Ausgabe 978-1-4612-1394-9 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009017107&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bonnans, J. Frédéric 1957- Shapiro, Alexander 1949- Perturbation analysis of optimization problems Operations research gtt Optimaliseren gtt Optimisation mathématique Perturbation (Mathématiques) Programação matemática larpcal Programação não linear larpcal Mathematical optimization Perturbation (Mathematics) Störungstheorie (DE-588)4128420-3 gnd Optimierung (DE-588)4043664-0 gnd |
| subject_GND | (DE-588)4128420-3 (DE-588)4043664-0 |
| title | Perturbation analysis of optimization problems |
| title_auth | Perturbation analysis of optimization problems |
| title_exact_search | Perturbation analysis of optimization problems |
| title_full | Perturbation analysis of optimization problems J. Frédéric Bonnans ; Alexander Shapiro |
| title_fullStr | Perturbation analysis of optimization problems J. Frédéric Bonnans ; Alexander Shapiro |
| title_full_unstemmed | Perturbation analysis of optimization problems J. Frédéric Bonnans ; Alexander Shapiro |
| title_short | Perturbation analysis of optimization problems |
| title_sort | perturbation analysis of optimization problems |
| topic | Operations research gtt Optimaliseren gtt Optimisation mathématique Perturbation (Mathématiques) Programação matemática larpcal Programação não linear larpcal Mathematical optimization Perturbation (Mathematics) Störungstheorie (DE-588)4128420-3 gnd Optimierung (DE-588)4043664-0 gnd |
| topic_facet | Operations research Optimaliseren Optimisation mathématique Perturbation (Mathématiques) Programação matemática Programação não linear Mathematical optimization Perturbation (Mathematics) Störungstheorie Optimierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009017107&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT bonnansjfrederic perturbationanalysisofoptimizationproblems AT shapiroalexander perturbationanalysisofoptimizationproblems |