Linear and nonlinear programming:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston [u.a.]
Kluwer Acad. Publ.
2003
|
| Ausgabe: | 2. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 491 S. graph. Darst. |
| ISBN: | 1402075936 9781402075933 |
Internformat
MARC
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| 245 | 1 | 0 | |a Linear and nonlinear programming |c David G. Luenberger |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Boston [u.a.] |b Kluwer Acad. Publ. |c 2003 | |
| 300 | |a XV, 491 S. |b graph. Darst. | ||
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Datensatz im Suchindex
| _version_ | 1804136448299892736 |
|---|---|
| adam_text | CONTENTS
Chapter
1
Introduction
1.1
Optimization
................ 1
1.2
Types of Problems
.............. 2
1.3
Size of Problems
............... 5
1.4
Iterative Algorithms and Convergence
....... 6
PART I Linear Programming
Chapter
2
Basic Properties of Linear Programs
2.1
Introduction
................ 11
2.2
Examples of Linear Programming Problems
..... 14
2.3
Basic Solutions
............... 17
2.4
The Fundamental Theorem of Linear Programming
... 18
2.5
Relations to Convexity
............ 21
2.6
Exercises
................. 26
Chapter
3
The Simplex Method
3.1
Pivots
.................. 30
3.2
Adjacent Extreme Points
............ 36
3.3
Determining a Minimum Feasible Solution
...... 40
3.4
Computational Procedure
—
Simplex Method
..... 44
3.5
Artificial Variables
.............. 48
*3.6 Variables with Upper Bounds
.......... 53
3.7
Matrix Form of the Simplex Method
........ 58
3.8
The Revised Simplex Method
.......... 59
*3.9 The Simplex Method and
LU
Decomposition
..... 65
3.10
Decomposition
............... 68
3.11
Summary
................. 75
3.12
Exercises
................. 76
xi
xii Contents
Chapter
4
Duality
4.1
Dual Linear Programs
............. 85
4.2
The Duality Theorem
............. 88
4.3
Relations to the Simplex Procedure
........ 90
4.4
Sensitivity and Complementary Slackness
...... 95
*4.5 The Dual Simplex Method
........... 97
*4.6 The Primal-Dual Algorithm
........... 99
*4.7 Reduction of Linear Inequalities
......... 104
4.8
Exercises
................. 110
Chapter
5
Transportation and Network Flow Problems
5.1
The Transportation Problem
........... 117
5.2
Finding a Basic Feasible Solution
......... 121
5.3
Basis Triangularity
.............. 123
5.4
Simplex Method for Transportation Problems
..... 126
5.5
The Assignment Problem
............ 133
5.6
Basic Network Concepts
............ 134
5.7
Minimum Cost Flow
............. 137
5.8
Maximal Flow
............... 141
*5.9 Primal-Dual Transportation Algorithm
....... 149
5.10
Summary
................. 157
5.11
Exercises
................. 158
PART II Unconstrained Problems
Chapter
6
Basic Properties of Solutions and Algorithms
6.1
First-Order Necessary Conditions
......... 168
6.2
Examples of Unconstrained Problems
....... 170
6.3
Second-Order Conditions
............ 174
6.4
Convex and Concave Functions
......... 176
6.5
Minimization and Maximization of Convex Functions
. . 180
6.6
Global Convergence of Descent Algorithms
..... 182
6.7
Speed of Convergence
............. 189
6.8
Summary
................. 193
6.9
Exercises
................. 194
Chapter
7
Basic Descent Methods
7.
1 Fibonacci and Golden Section Search
....... 197
7.2
Line Search by Curve Fitting
.......... 200
7.3
Global Convergence of Curve Fitting
........ 207
7.4
Closedness of Line Search Algorithms
....... 209
7.5
Inaccurate Line Search
............ 211
7.6
The Method of Steepest Descent
......... 214
7.7
Applications of the Theory
........... 220
7.8
Newton s Method
.............. 225
Contents
xiii
7.9
Coordinate Descent Methods
.......... 227
7.10
Spacer Steps
................ 230
7.11
Summary
................. 231
7.12
Exercises
................. 232
Chapter
8
Conjugate Direction Methods
8.1
Conjugate Directions
............. 238
8.2
Descent Properties of the Conjugate Direction Method
. . 241
8.3
The Conjugate Gradient Method
......... 243
8.4
The Conjugate Gradient Method as an Optimal Process
. . 246
8.5
The Partial Conjugate Gradient Method
....... 248
8.6
Extension to Nonquadratic Problems
........ 252
8.7
Parallel Tangents
.............. 254
8.8
Exercises
................. 257
Chapter
9
Quasi-Newton
Methods
9.1
Modified Newton Method
........... 261
9.2
Construction of the Inverse
........... 263
9.3
Davidon-Fletcher-Powell Method
......... 265
9.4
The Broyden Family
............. 268
9.5
Convergence Properties
............ 271
*9.6 Scaling
.................. 275
9.7
Memoryless
Quasi-Newton
Methods
........ 279
9.8
Combination of Steepest Descent and Newton s Method
. 282
9.9
Summary
................. 287
9.10
Exercises
................. 288
PART III Constrained Minimization
Chapter
10
Constrained Minimization Conditions
10.1
Constraints
................ 295
10.2
Tangent Plane
............... 297
10.3
First-Order Necessary Conditions (Equality Constraints)
. 300
10.4
Examples
................. 301
10.5
Second-Order Conditions
............ 306
10.6
Eigenvalues in Tangent Subspace
......... 308
10.7
Sensitivity
................. 312
10.8
Inequality Constraints
............. 314
10.9
Summary
................. 318
10.10
Exercises
................. 318
Chapter
11
Primal Methods
11.1
Advantage of Primal Methods
.......... 322
11.2
Feasible Direction Methods
........... 323
11.3
Active Set Methods
............. 326
xiv Contents
11.4 The Gradient
Projection Method
......... 330
11.5
Convergence Rate of the Gradient Projection Method
. . 337
11.6
The Reduced Gradient Method
.......... 345
11.7
Convergence Rate of the Reduced Gradient Method
... 350
11.8
Variations
................. 357
11.9
Summary
................. 359
11.10
Exercises
................. 360
Chapter
12
Penalty and Barrier Methods
12.1
Penalty Methods
............... 366
12.2
Barrier Methods
............... 369
12.3
Properties of Penalty and Barrier Functions
..... 371
12.4
Newton s Method and Penalty Functions
...... 378
12.5
Conjugate Gradients and Penalty Methods
...... 380
12.6
Normalization of Penalty Functions
........ 382
*12.7 Penalty Functions and Gradient Projection
...... 384
12.8
Exact Penalty Functions
............ 387
12.9
Summary
................. 391
12.10
Exercises
................. 392
Chapter
13
Dual and Cutting Plane Methods
13.1
Local Duality
................ 397
13.2
Dual Canonical Convergence Rate
......... 402
13.3
Separable Problems
.............. 403
13.4
Augmented Lagrangians
............ 406
13.5
The Dual Viewpoint
............. 411
13.6
Cutting Plane Methods
............ 416
13.7
Kelley s Convex Cutting Plane Algorithm
...... 418
13.8
Modifications
................ 420
13.9
Exercises
................. 421
Chapter
14 Lagrange
Methods
14.1
Quadratic Programming
............ 423
14.2
Direct Methods
............... 427
14.3
Relation to Quadratic Programming
........ 433
14.4
Modified Newton Methods
.....;..... 435
14.5
Descent Properties
.............. 439
14.6
Rate of Convergence
............. 444
14.7
Quasi-Newton
Methods
............ 446
14.8
Summary
................. 449
14.9
Exercises
................. 450
Appendix A Mathematical Review
A.I Sets
................... 455
A.2 Matrix Notation
............... 456
A.3 Spaces
.................. 457
Contents xv
A.4
Eigenvalues and Quadratic Forms
......... 458
A.5 Topological Concepts
............. 459
A.
6
Functions
................. 460
Appendix
В
Convex Sets
B.I Basic Definitions
.............. 464
B.2
Hyperplanes
and Polytopes
........... 465
B.3 Separating and Supporting
Hyperplanes....... 468
В.
4
Extreme Points
............... 470
Appendix
С
Gaussian Elimination
Bibliography
..................... 476
Index
..................... 487
|
| adam_txt |
CONTENTS
Chapter
1
Introduction
1.1
Optimization
. 1
1.2
Types of Problems
. 2
1.3
Size of Problems
. 5
1.4
Iterative Algorithms and Convergence
. 6
PART I Linear Programming
Chapter
2
Basic Properties of Linear Programs
2.1
Introduction
. 11
2.2
Examples of Linear Programming Problems
. 14
2.3
Basic Solutions
. 17
2.4
The Fundamental Theorem of Linear Programming
. 18
2.5
Relations to Convexity
. 21
2.6
Exercises
. 26
Chapter
3
The Simplex Method
3.1
Pivots
. 30
3.2
Adjacent Extreme Points
. 36
3.3
Determining a Minimum Feasible Solution
. 40
3.4
Computational Procedure
—
Simplex Method
. 44
3.5
Artificial Variables
. 48
*3.6 Variables with Upper Bounds
. 53
3.7
Matrix Form of the Simplex Method
. 58
3.8
The Revised Simplex Method
. 59
*3.9 The Simplex Method and
LU
Decomposition
. 65
3.10
Decomposition
. 68
3.11
Summary
. 75
3.12
Exercises
. 76
xi
xii Contents
Chapter
4
Duality
4.1
Dual Linear Programs
. 85
4.2
The Duality Theorem
. 88
4.3
Relations to the Simplex Procedure
. 90
4.4
Sensitivity and Complementary Slackness
. 95
*4.5 The Dual Simplex Method
. 97
*4.6 The Primal-Dual Algorithm
. 99
*4.7 Reduction of Linear Inequalities
. 104
4.8
Exercises
. 110
Chapter
5
Transportation and Network Flow Problems
5.1
The Transportation Problem
. 117
5.2
Finding a Basic Feasible Solution
. 121
5.3
Basis Triangularity
. 123
5.4
Simplex Method for Transportation Problems
. 126
5.5
The Assignment Problem
. 133
5.6
Basic Network Concepts
. 134
5.7
Minimum Cost Flow
. 137
5.8
Maximal Flow
. 141
*5.9 Primal-Dual Transportation Algorithm
. 149
5.10
Summary
. 157
5.11
Exercises
. 158
PART II Unconstrained Problems
Chapter
6
Basic Properties of Solutions and Algorithms
6.1
First-Order Necessary Conditions
. 168
6.2
Examples of Unconstrained Problems
. 170
6.3
Second-Order Conditions
. 174
6.4
Convex and Concave Functions
. 176
6.5
Minimization and Maximization of Convex Functions
. . 180
6.6
Global Convergence of Descent Algorithms
. 182
6.7
Speed of Convergence
. 189
6.8
Summary
. 193
6.9
Exercises
. 194
Chapter
7
Basic Descent Methods
7.
1 Fibonacci and Golden Section Search
. 197
7.2
Line Search by Curve Fitting
. 200
7.3
Global Convergence of Curve Fitting
. 207
7.4
Closedness of Line Search Algorithms
. 209
7.5
Inaccurate Line Search
. 211
7.6
The Method of Steepest Descent
. 214
7.7
Applications of the Theory
. 220
7.8
Newton's Method
. 225
Contents
xiii
7.9
Coordinate Descent Methods
. 227
7.10
Spacer Steps
. 230
7.11
Summary
. 231
7.12
Exercises
. 232
Chapter
8
Conjugate Direction Methods
8.1
Conjugate Directions
. 238
8.2
Descent Properties of the Conjugate Direction Method
. . 241
8.3
The Conjugate Gradient Method
. 243
8.4
The Conjugate Gradient Method as an Optimal Process
. . 246
8.5
The Partial Conjugate Gradient Method
. 248
8.6
Extension to Nonquadratic Problems
. 252
8.7
Parallel Tangents
. 254
8.8
Exercises
. 257
Chapter
9
Quasi-Newton
Methods
9.1
Modified Newton Method
. 261
9.2
Construction of the Inverse
. 263
9.3
Davidon-Fletcher-Powell Method
. 265
9.4
The Broyden Family
. 268
9.5
Convergence Properties
. 271
*9.6 Scaling
. 275
9.7
Memoryless
Quasi-Newton
Methods
. 279
9.8
Combination of Steepest Descent and Newton's Method
. 282
9.9
Summary
. 287
9.10
Exercises
. 288
PART III Constrained Minimization
Chapter
10
Constrained Minimization Conditions
10.1
Constraints
. 295
10.2
Tangent Plane
. 297
10.3
First-Order Necessary Conditions (Equality Constraints)
. 300
10.4
Examples
. 301
10.5
Second-Order Conditions
. 306
10.6
Eigenvalues in Tangent Subspace
. 308
10.7
Sensitivity
. 312
10.8
Inequality Constraints
. 314
10.9
Summary
. 318
10.10
Exercises
. 318
Chapter
11
Primal Methods
11.1
Advantage of Primal Methods
. 322
11.2
Feasible Direction Methods
. 323
11.3
Active Set Methods
. 326
xiv Contents
11.4 The Gradient
Projection Method
. 330
11.5
Convergence Rate of the Gradient Projection Method
. . 337
11.6
The Reduced Gradient Method
. 345
11.7
Convergence Rate of the Reduced Gradient Method
. 350
11.8
Variations
. 357
11.9
Summary
. 359
11.10
Exercises
. 360
Chapter
12
Penalty and Barrier Methods
12.1
Penalty Methods
. 366
12.2
Barrier Methods
. 369
12.3
Properties of Penalty and Barrier Functions
. 371
12.4
Newton's Method and Penalty Functions
. 378
12.5
Conjugate Gradients and Penalty Methods
. 380
12.6
Normalization of Penalty Functions
. 382
*12.7 Penalty Functions and Gradient Projection
. 384
12.8
Exact Penalty Functions
. 387
12.9
Summary
. 391
12.10
Exercises
. 392
Chapter
13
Dual and Cutting Plane Methods
13.1
Local Duality
. 397
13.2
Dual Canonical Convergence Rate
. 402
13.3
Separable Problems
. 403
13.4
Augmented Lagrangians
. 406
13.5
The Dual Viewpoint
. 411
13.6
Cutting Plane Methods
. 416
13.7
Kelley's Convex Cutting Plane Algorithm
. 418
13.8
Modifications
. 420
13.9
Exercises
. 421
Chapter
14 Lagrange
Methods
14.1
Quadratic Programming
. 423
14.2
Direct Methods
. 427
14.3
Relation to Quadratic Programming
. 433
14.4
Modified Newton Methods
.;. 435
14.5
Descent Properties
. 439
14.6
Rate of Convergence
. 444
14.7
Quasi-Newton
Methods
. 446
14.8
Summary
. 449
14.9
Exercises
. 450
Appendix A Mathematical Review
A.I Sets
. 455
A.2 Matrix Notation
. 456
A.3 Spaces
. 457
Contents xv
A.4
Eigenvalues and Quadratic Forms
. 458
A.5 Topological Concepts
. 459
A.
6
Functions
. 460
Appendix
В
Convex Sets
B.I Basic Definitions
. 464
B.2
Hyperplanes
and Polytopes
. 465
B.3 Separating and Supporting
Hyperplanes. 468
В.
4
Extreme Points
. 470
Appendix
С
Gaussian Elimination
Bibliography
. 476
Index
. 487 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Luenberger, David G. |
| author_facet | Luenberger, David G. |
| author_role | aut |
| author_sort | Luenberger, David G. |
| author_variant | d g l dg dgl |
| building | Verbundindex |
| bvnumber | BV022390269 |
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| callnumber-subject | T - General Technology |
| classification_rvk | SK 870 |
| ctrlnum | (OCoLC)123303611 (DE-599)BVBBV022390269 |
| dewey-full | 519.7/2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.7/2 |
| dewey-search | 519.7/2 |
| dewey-sort | 3519.7 12 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV022390269 |
| illustrated | Illustrated |
| index_date | 2024-07-02T17:14:25Z |
| indexdate | 2024-07-09T20:56:33Z |
| institution | BVB |
| isbn | 1402075936 9781402075933 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015599116 |
| oclc_num | 123303611 |
| open_access_boolean | |
| owner | DE-29T DE-355 DE-BY-UBR DE-83 |
| owner_facet | DE-29T DE-355 DE-BY-UBR DE-83 |
| physical | XV, 491 S. graph. Darst. |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Kluwer Acad. Publ. |
| record_format | marc |
| spelling | Luenberger, David G. Verfasser aut Linear and nonlinear programming David G. Luenberger 2. ed. Boston [u.a.] Kluwer Acad. Publ. 2003 XV, 491 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Linear programming Nonlinear programming Lineare Ordnung (DE-588)4167706-7 gnd rswk-swf Nichtlineare Optimierung (DE-588)4128192-5 gnd rswk-swf Lineare Optimierung (DE-588)4035816-1 gnd rswk-swf Optimierung (DE-588)4043664-0 gnd rswk-swf Lineare Ordnung (DE-588)4167706-7 s Nichtlineare Optimierung (DE-588)4128192-5 s 1\p DE-604 Lineare Optimierung (DE-588)4035816-1 s 2\p DE-604 Optimierung (DE-588)4043664-0 s 3\p DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015599116&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 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Luenberger, David G. Linear and nonlinear programming Linear programming Nonlinear programming Lineare Ordnung (DE-588)4167706-7 gnd Nichtlineare Optimierung (DE-588)4128192-5 gnd Lineare Optimierung (DE-588)4035816-1 gnd Optimierung (DE-588)4043664-0 gnd |
| subject_GND | (DE-588)4167706-7 (DE-588)4128192-5 (DE-588)4035816-1 (DE-588)4043664-0 |
| title | Linear and nonlinear programming |
| title_auth | Linear and nonlinear programming |
| title_exact_search | Linear and nonlinear programming |
| title_exact_search_txtP | Linear and nonlinear programming |
| title_full | Linear and nonlinear programming David G. Luenberger |
| title_fullStr | Linear and nonlinear programming David G. Luenberger |
| title_full_unstemmed | Linear and nonlinear programming David G. Luenberger |
| title_short | Linear and nonlinear programming |
| title_sort | linear and nonlinear programming |
| topic | Linear programming Nonlinear programming Lineare Ordnung (DE-588)4167706-7 gnd Nichtlineare Optimierung (DE-588)4128192-5 gnd Lineare Optimierung (DE-588)4035816-1 gnd Optimierung (DE-588)4043664-0 gnd |
| topic_facet | Linear programming Nonlinear programming Lineare Ordnung Nichtlineare Optimierung Lineare Optimierung Optimierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015599116&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT luenbergerdavidg linearandnonlinearprogramming |