Robust optimization:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Princeton ; Oxford
Princeton University Press
[2009]
|
| Schriftenreihe: | Princeton series in applied mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xxii, 542 Seiten Illustrationen |
| ISBN: | 9780691143682 |
Internformat
MARC
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| 100 | 1 | |a Ben-Tal, Aharon |e Verfasser |0 (DE-588)170328007 |4 aut | |
| 245 | 1 | 0 | |a Robust optimization |c Aharon Ben-Tal, Laurent El Ghaoui, Arkadi Nemirovski |
| 264 | 1 | |a Princeton ; Oxford |b Princeton University Press |c [2009] | |
| 264 | 4 | |c © 2009 | |
| 300 | |a xxii, 542 Seiten |b Illustrationen | ||
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Datensatz im Suchindex
| _version_ | 1804140854333407232 |
|---|---|
| adam_text | Contents
Preface
PART I. ROBUST LINEAR OPTIMIZATION
1
Chapter
1.
Uncertain Linear Optimization Problems and their
Robust Counterparts
3
1.1
Data Uncertainty in Linear Optimization
3
1.2
Uncertain Linear Problems and their Robust Counterparts
7
1.3
Tractability of Robust Counterparts
16
1.4
Non-Affine Perturbations
23
1.5
Exercises
25
1.6
Notes and Remarks
25
Chapter
2.
Robust Counterpart Approximations of Scalar Chance
Constraints
27
2.1
How to Specify an Uncertainty Set
27
2.2
Chance Constraints and their Safe Tractable Approximations
28
2.3
Safe Tractable Approximations of Scalar Chance
Constraints: Basic Examples
31
2.4
Extensions
44
2.5
Exercises
60
2.6
Notes and Remarks
64
Chapter
3.
Globalized Robust Counterparts of Uncertain
LO
Prob¬
lems
67
3.1
Globalized Robust Counterpart
—
Motivation and Definition
67
3.2
Computational Tractability of GRC
69
3.3
Example: Synthesis of Antenna Arrays
70
3.4
Exercises
79
3.5
Notes and Remarks
79
Chapter
4.
More on Safe Tractable Approximations of Scalar
Chance Constraints
81
vi
CONTENTS
4.1
Robust Counterpart Representation of a Safe Convex
Approximation to a Scalar Chance Constraint
81
4.2
Bernstein Approximation of a Chance Constraint
83
4.3
From Bernstein Approximation to Conditional Value at Risk
and Back
90
4.4
Majorization
105
4.5
Beyond the Case of Independent Linear Perturbations
109
4.6
Exercises
136
4.7
Notes and Remarks
145
PART II. ROBUST CONIC OPTIMIZATION
147
Chapter
5.
Uncertain Conic Optimization: The Concepts
149
5.1
Uncertain Conic Optimization: Preliminaries
149
5.2
Robust Counterpart of Uncertain Conic Problem: Tractability
151
5.3
Safe Tractable Approximations of RCs of Uncertain Conic
Inequalities
153
5.4
Exercises
156
5.5
Notes and Remarks
157
Chapter
6.
Uncertain Conic Quadratic Problems with Tractable
RCs
159
6.1
A Generic Solvable Case: Scenario Uncertainty
159
6.2
Solvable Case I: Simple Interval Uncertainty
160
6.3
Solvable Case II: Unstructured Norm-Bounded Uncertainty
161
6.4
Solvable Case III: Convex Quadratic Inequality with Un¬
structured Norm-Bounded Uncertainty
165
6.5
Solvable Case IV: CQI with Simple Ellipsoidal Uncertainty
167
6.6
Illustration: Robust Linear Estimation
173
6.7
Exercises
178
6.8
Notes and Remarks
178
Chapter
7.
Approximating RCs of Uncertain Conic Quadratic
Problems
179
7.1
Structured Norm-Bounded Uncertainty
179
7.2
The Case of
П
-Ellipsoidal Uncertainty
195
7.3
Exercises
201
7.4
Notes and Remarks
201
Chapter
8.
Uncertain
Semidefinite
Problems with Tractable RCs
203
8.1
Uncertain
Semidefinite
Problems
203
8.2
Tractability of RCs of Uncertain
Semidefinite
Problems
204
8.3
Exercises
222
CONTENTS
vii
8.4 Notes
and Remarks
222
Chapter
9.
Approximating RCs of Uncertain
Semidefinite
Problems
225
9.1
Tight Tractable Approximations of RCs of Uncertain SDPs
with Structured Norm-Bounded Uncertainty
225
9.2
Exercises
232
9.3
Notes and Remarks
234
Chapter
10.
Approximating Chance Constrained CQIs and LMIs
235
10.1
Chance Constrained LMIs
235
10.2
The Approximation Scheme
240
10.3
Gaussian Majorization
252
10.4
Chance Constrained LMIs: Special Cases
255
10.5
Notes and Remarks
276
Chapter
11.
Globalized Robust Counterparts of Uncertain Conic
Problems
279
11.1
Globalized Robust Counterparts of Uncertain Conic
Problems: Definition
279
11.2
Safe Tractable Approximations of GRCs
281
11.3
GRC of Uncertain Constraint: Decomposition
282
11.4
Tractability of GRCs
284
11.5
Illustration: Robust Analysis of
Nonexpansive
Dynamical
Systems
292
Chapter
12.
Robust Classification and Estimation
301
12.1
Robust Support Vector Machines
301
12.2
Robust Classification and Regression
309
12.3 Affine
Uncertainty Models
325
12.4
Random
Affine
Uncertainty Models
331
12.5
Exercises
336
12.6
Notes and remarks
337
PART III. ROBUST MULTI-STAGE OPTIMIZATION
339
Chapter
13.
Robust Markov Decision Processes
341
13.1
Markov Decision Processes
341
13.2
The Robust MDP Problems
345
13.3
The Robust Bellman Recursion on Finite Horizon
347
13.4
Notes and Remarks
352
Chapter
14.
Robust Adjustable Multistage Optimization
355
viii CONTENTS
14.1
Adjustable Robust Optimization: Motivation
355
14.2
Adjustable Robust Counterpart
357
14.3
Affinely Adjustable Robust Counterparts
368
14.4
Adjustable Robust Optimization and Synthesis of Linear
Controllers
392
14.5
Exercises
408
14.6
Notes and Remarks
411
PART IV. SELECTED APPLICATIONS
415
Chapter
15.
Selected Applications
417
15.1
Robust Linear Regression and Manufacturing of TV Tubes
417
15.2
Inventory Management with Flexible Commitment Contracts
421
15.3
Controlling a Multi-Echelon Multi-Period Supply Chain
432
Appendix A. Notation and Prerequisites
447
A.I Notation
447
A.
2
Conic Programming
448
A.3 Efficient Solvability of Convex Programming
460
469
469
481
483
489
506
511
511
511
513
513
516
519
520
521
523
525
527
531
Index
539
Appendix B. Some Auxiliary Proofs
B.I
Proofs for Chapter
4
B.2
S-Lemma
B.3
Approximate S-Lemma
B.4
Matrix Cube Theorem
B.5
Proofs for Chapter
10
Appendix C. Solutions to Selected Exercises
C.I
Chapter
1
C.2
Chapter
2
C.3
Chapter
3
C.4
Chapter
4
C.5
Chapter
5
C.6
Chapter
6
C.7
Chapter
7
C.8
Chapter
8
C.9
Chapter
9
CIO
Chapter
12
СП
Chapter
14
Bibliography
|
| any_adam_object | 1 |
| author | Ben-Tal, Aharon El Ghaoui, Laurent Nemirovskij, Arkadij S. 1947- |
| author_GND | (DE-588)170328007 (DE-588)1089236522 (DE-588)12209395X |
| author_facet | Ben-Tal, Aharon El Ghaoui, Laurent Nemirovskij, Arkadij S. 1947- |
| author_role | aut aut aut |
| author_sort | Ben-Tal, Aharon |
| author_variant | a b t abt g l e gl gle a s n as asn |
| building | Verbundindex |
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| callnumber-search | QA402.5 |
| callnumber-sort | QA 3402.5 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 870 QH 233 QH 420 |
| classification_tum | MAT 494f |
| ctrlnum | (OCoLC)318672208 (DE-599)BVBBV035876939 |
| dewey-full | 519.6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.6 |
| dewey-search | 519.6 |
| dewey-sort | 3519.6 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV035876939 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:06:35Z |
| institution | BVB |
| isbn | 9780691143682 |
| language | English |
| lccn | 2009013229 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018734607 |
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| physical | xxii, 542 Seiten Illustrationen |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Princeton University Press |
| record_format | marc |
| series2 | Princeton series in applied mathematics |
| spelling | Ben-Tal, Aharon Verfasser (DE-588)170328007 aut Robust optimization Aharon Ben-Tal, Laurent El Ghaoui, Arkadi Nemirovski Princeton ; Oxford Princeton University Press [2009] © 2009 xxii, 542 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Princeton series in applied mathematics Robust optimization Linear programming Robuste Optimierung (DE-588)7752811-6 gnd rswk-swf Optimierung (DE-588)4043664-0 gnd rswk-swf Robustheit (DE-588)4126481-2 gnd rswk-swf Unsicherheit (DE-588)4186957-6 gnd rswk-swf Robuste Statistik (DE-588)4451047-0 gnd rswk-swf Lineare Optimierung (DE-588)4035816-1 gnd rswk-swf Robuste Statistik (DE-588)4451047-0 s Lineare Optimierung (DE-588)4035816-1 s DE-604 Optimierung (DE-588)4043664-0 s Unsicherheit (DE-588)4186957-6 s Robustheit (DE-588)4126481-2 s DE-188 Robuste Optimierung (DE-588)7752811-6 s 1\p DE-604 El Ghaoui, Laurent Verfasser (DE-588)1089236522 aut Nemirovskij, Arkadij S. 1947- Verfasser (DE-588)12209395X aut Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018734607&sequence=000002&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 | Ben-Tal, Aharon El Ghaoui, Laurent Nemirovskij, Arkadij S. 1947- Robust optimization Robust optimization Linear programming Robuste Optimierung (DE-588)7752811-6 gnd Optimierung (DE-588)4043664-0 gnd Robustheit (DE-588)4126481-2 gnd Unsicherheit (DE-588)4186957-6 gnd Robuste Statistik (DE-588)4451047-0 gnd Lineare Optimierung (DE-588)4035816-1 gnd |
| subject_GND | (DE-588)7752811-6 (DE-588)4043664-0 (DE-588)4126481-2 (DE-588)4186957-6 (DE-588)4451047-0 (DE-588)4035816-1 |
| title | Robust optimization |
| title_auth | Robust optimization |
| title_exact_search | Robust optimization |
| title_full | Robust optimization Aharon Ben-Tal, Laurent El Ghaoui, Arkadi Nemirovski |
| title_fullStr | Robust optimization Aharon Ben-Tal, Laurent El Ghaoui, Arkadi Nemirovski |
| title_full_unstemmed | Robust optimization Aharon Ben-Tal, Laurent El Ghaoui, Arkadi Nemirovski |
| title_short | Robust optimization |
| title_sort | robust optimization |
| topic | Robust optimization Linear programming Robuste Optimierung (DE-588)7752811-6 gnd Optimierung (DE-588)4043664-0 gnd Robustheit (DE-588)4126481-2 gnd Unsicherheit (DE-588)4186957-6 gnd Robuste Statistik (DE-588)4451047-0 gnd Lineare Optimierung (DE-588)4035816-1 gnd |
| topic_facet | Robust optimization Linear programming Robuste Optimierung Optimierung Robustheit Unsicherheit Robuste Statistik Lineare Optimierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018734607&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT bentalaharon robustoptimization AT elghaouilaurent robustoptimization AT nemirovskijarkadijs robustoptimization |