Convex optimization:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2012
|
| Edition: | 10. print. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturangaben Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | xiii, 716 Seiten Illustrationen 28cm |
| ISBN: | 9780521833783 |
Staff View
MARC
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| 100 | 1 | |a Boyd, Stephen P. |d 1958- |e Verfasser |0 (DE-588)129723177 |4 aut | |
| 245 | 1 | 0 | |a Convex optimization |c Stephen Boyd, Lieven Vandenberghe |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-025200235 | ||
Record in the Search Index
| _version_ | 1804149381583077376 |
|---|---|
| adam_text | Contents
Preface
xi
1
Introduction
1
1.1
Mathematical optimization
........................ 1
1.2
Least-squares and linear programming
.................. 4
1.3
Convex optimization
............................ 7
1.4
Nonlinear optimization
.......................... 9
1.5
Outline
................................... 11
1.6
Notation
.................................. 14
Bibliography
................................... 16
1 Theory
19
2
Convex sets
21
2.1 Affine
and convex sets
........................... 21
2.2
Some important examples
......................... 27
2.3
Operations that preserve convexity
.................... 35
2.4
Generalized inequalities
.......................... 43
2.5
Separating and supporting
hyperplanes.................. 46
2.6
Dual cones and generalized inequalities
.................. 51
Bibliography
................................... 59
Exercises
..................................... 60
3
Convex functions
67
3.1
Basic properties and examples
...................... 67
3.2
Operations that preserve convexity
.................... 79
3.3
The conjugate function
.......................... 90
3.4
Quasiconvex functions
........................... 95
3.5
Log-concave and log-convex functions
.................. 104
3.6
Convexity with respect to generalized inequalities
............ 108
Bibliography
................................... 112
Exercises
..................................... 113
Convex
optimization problems
127
4.1
Optimization problems
.......................... 127
4.2
Convex optimization
............................ 136
4.3
Linear optimization problems
....................... 146
4.4
Quadratic optimization problems
..................... 152
4.5
Geometric programming
.......................... 160
4.6
Generalized inequality constraints
..................... 167
4.7
Vector optimization
............................ 174
Bibliography
................................... 188
Exercises
..................................... 189
Duality
215
5.1
The
Lagrange
dual function
........................ 215
5.2
The
Lagrange
dual problem
........................ 223
5.3
Geometric interpretation
......................... 232
5.4
Saddle-point interpretation
........................ 237
5.5
Optimality conditions
........................... 241
5.6
Perturbation and sensitivity analysis
................... 249
5.7
Examples
.................................. 253
5.8
Theorems of alternatives
......................... 258
5.9
Generalized inequalities
.......................... 264
Bibliography
................................... 272
Exercises
..................................... 273
Applications
289
Approximation and fitting
291
6.1
Norm approximation
............................291
6.2
Least-norm problems
...........................302
6.3
Regularized approximation
........................305
6.4
Robust approximation
...........................318
6.5
Function fitting and interpolation
.....................324
Bibliography
...................................343
Exercises
.....................................344
Statistical estimation
351
7.1
Parametric distribution estimation
....................351
7.2
Nonparametric distribution estimation
..................359
7.3
Optimal detector design and hypothesis testing
.............364
7.4
Chebyshev and Chernoff bounds
.....................374
7.5
Experiment design
.............................384
Bibliography
...................................392
Exercises
.....................................393
Geometrie
problems
397
8.1
Projection on a set
............................397
8.2
Distance between sets
...........................402
8.3
Euclidean distance and angle problems
..................405
8.4
Extremal volume ellipsoids
........................410
8.5
Centering
.................................416
8.6
Classification
................................422
8.7
Placement and location
..........................432
8.8
Floor planning
...............................438
Bibliography
...................................446
Exercises
.....................................447
III Algorithms
455
9
Unconstrained minimization
457
9.1
Unconstrained minimization problems
..................457
9.2
Descent methods
.............................463
9.3
Gradient descent method
.........................466
9.4
Steepest descent method
.........................475
9.5
Newton s method
.............................484
9.6
Self-concordance
..............................496
9.7
Implementation
..............................508
Bibliography
...................................513
Exercises
.....................................514
10
Equality constrained minimization
521
10.1
Equality constrained minimization problems
...............521
10.2
Newton s method with equality constraints
................525
10.3
Infeasible start Newton method
......................531
10.4
Implementation
..............................542
Bibliography
...................................556
Exercises
.....................................557
11
Interior-point methods
561
11.1
Inequality constrained minimization problems
..............561
11.2
Logarithmic barrier function and central path
..............562
11.3
The barrier method
............................568
11.4
Feasibility and phase I methods
......................579
11.5
Complexity analysis via self-concordance
.................585
11.6
Problems with generalized inequalities
..................596
11.7
Primal-dual interior-point methods
....................609
11.8
Implementation
..............................615
Bibliography
...................................621
Exercises
.....................................623
Appendices
631
A Mathematical background
633
A.I Norms
................................... 633
A.2 Analysis
.................................. 637
A.3 Functions
................................. 639
A.
4
Derivatives
................................. 640
A.
5
Linear algebra
............................... 645
Bibliography
................................... 652
В
Problems involving two quadratic functions
653
B.I Single constraint quadratic optimization
.................653
B.2 The S-procedure
..............................655
B.3 The field of values of two symmetric matrices
..............656
B.4 Proofs of the strong duality results
....................657
Bibliography
...................................659
С
Numerical linear algebra background
661
C.I Matrix structure and algorithm complexity
................661
C.2 Solving linear equations with factored matrices
..............664
C.3
LU, Cholesky,
and LDLT factorization
..................668
C.4 Block elimination and
Schur
complements
................672
C.5 Solving underdetermined linear equations
.................681
Bibliography
...................................684
References
685
Notation
697
Index
701
|
| any_adam_object | 1 |
| author | Boyd, Stephen P. 1958- Vandenberghe, Lieven 1964- |
| author_GND | (DE-588)129723177 (DE-588)135800595 |
| author_facet | Boyd, Stephen P. 1958- Vandenberghe, Lieven 1964- |
| author_role | aut aut |
| author_sort | Boyd, Stephen P. 1958- |
| author_variant | s p b sp spb l v lv |
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| bvnumber | BV040346081 |
| classification_rvk | SK 870 |
| ctrlnum | (OCoLC)796759285 (DE-599)BVBBV040346081 |
| discipline | Mathematik |
| edition | 10. print. |
| format | Book |
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| genre_facet | Lehrbuch |
| id | DE-604.BV040346081 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:22:08Z |
| institution | BVB |
| isbn | 9780521833783 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025200235 |
| oclc_num | 796759285 |
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| owner | DE-739 |
| owner_facet | DE-739 |
| physical | xiii, 716 Seiten Illustrationen 28cm |
| publishDate | 2012 |
| publishDateSearch | 2012 |
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| publisher | Cambridge University Press |
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| spelling | Boyd, Stephen P. 1958- Verfasser (DE-588)129723177 aut Convex optimization Stephen Boyd, Lieven Vandenberghe 10. print. Cambridge Cambridge University Press 2012 xiii, 716 Seiten Illustrationen 28cm txt rdacontent n rdamedia nc rdacarrier Literaturangaben Hier auch später erschienene, unveränderte Nachdrucke Konvexe Optimierung (DE-588)4137027-2 gnd rswk-swf Algorithmentheorie (DE-588)4200409-3 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Konvexe Optimierung (DE-588)4137027-2 s Algorithmentheorie (DE-588)4200409-3 s DE-604 Vandenberghe, Lieven 1964- Verfasser (DE-588)135800595 aut Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025200235&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Boyd, Stephen P. 1958- Vandenberghe, Lieven 1964- Convex optimization Konvexe Optimierung (DE-588)4137027-2 gnd Algorithmentheorie (DE-588)4200409-3 gnd |
| subject_GND | (DE-588)4137027-2 (DE-588)4200409-3 (DE-588)4123623-3 |
| title | Convex optimization |
| title_auth | Convex optimization |
| title_exact_search | Convex optimization |
| title_full | Convex optimization Stephen Boyd, Lieven Vandenberghe |
| title_fullStr | Convex optimization Stephen Boyd, Lieven Vandenberghe |
| title_full_unstemmed | Convex optimization Stephen Boyd, Lieven Vandenberghe |
| title_short | Convex optimization |
| title_sort | convex optimization |
| topic | Konvexe Optimierung (DE-588)4137027-2 gnd Algorithmentheorie (DE-588)4200409-3 gnd |
| topic_facet | Konvexe Optimierung Algorithmentheorie Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025200235&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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