Linear and nonlinear programming:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY
Springer
2008
|
| Edition: | 3. ed. |
| Series: | International series in operations research & management science
116 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Auch als Internetausgabe |
| Physical Description: | XIII, 546 S. Ill., graph. Darst. |
| ISBN: | 9780387745022 0387745025 9780387745039 |
Staff View
MARC
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| 100 | 1 | |a Luenberger, David G. |d 1937- |e Verfasser |0 (DE-588)135911338 |4 aut | |
| 245 | 1 | 0 | |a Linear and nonlinear programming |c David G. Luenberger ; Yinyu Ye |
| 250 | |a 3. ed. | ||
| 264 | 1 | |a New York, NY |b Springer |c 2008 | |
| 300 | |a XIII, 546 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a International series in operations research & management science |v 116 | |
| 500 | |a Auch als Internetausgabe | ||
| 650 | 4 | |a Linear programming | |
| 650 | 4 | |a Nonlinear programming | |
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Record in the Search Index
| _version_ | 1804137220997644288 |
|---|---|
| adam_text | CONTENTS
Chapter
1.
Introduction
1.1.
Optimization
1.2.
Types of Problems
1.3.
Size of Problems
1.4.
Iterative Algorithms and Convergence
PART I Linear Programming
Chapter
2.
Chapter
3.
Chapter
4.
Basic Properties of Linear Programs
11
2.1.
Introduction
11
2.2.
Examples of Linear Programming Problems
14
2.3.
Basic Solutions
19
2.4.
The Fundamental Theorem of Linear Programming
20
2.5.
Relations to Convexity
22
2.6.
Exercises
28
The
Simplex Method
33
3.1.
Pivots
33
3.2.
Adjacent Extreme Points
38
3.3.
Determining a Minimum Feasible Solution
42
3.4.
Computational Procedure
—
Simplex Method
46
3.5.
Artificial Variables
50
3.6.
Matrix Form of the Simplex Method
54
3.7.
The Revised Simplex Method
56
3.8.
The Simplex Method and
LU
Decomposition
59
3.9.
Decomposition
62
3.10.
Summary
70
3.11.
Exercises
70
Duality
79
4.1.
Dual Linear Programs
79
4.2.
The Duality Theorem
82
4.3.
Relations to the Siirrolex Procedure
84
4.4.
Sensitivity and Complementary Slackness
*4.5. The Dual Simplex Method
ix
90
Contents
Chapter
5.
Chapter
6.
4.6.
The Primal-Dual Algorithm
93
*4.7.
Reduction of Linear Inequalities
98
4.8.
Exercises
103
Interior-Point Methods
111
5.1.
Elements of Complexity Theory
112
*5.2.
The Simplex Method is not Polynomial-Time
114
*5.3.
The Ellipsoid Method
115
5.4.
The Analytic Center
118
5.5.
The Central Path
121
5.6.
Solution Strategies
126
5.7.
Termination and Initialization
134
5.8.
Summary
139
5.9.
Exercises
140
Transportation and Network Flow Problems
145
6.1.
The Transportation Problem
145
6.2.
Finding a Basic Feasible Solution
148
6.3.
Basis Triangularity
150
6.4.
Simplex Method for Transportation Problems
153
6.5.
The Assignment Problem
159
6.6.
Basic Network Concepts
160
6.7.
Minimum Cost Flow
162
6.8.
Maximal Flow
166
6.9.
Summary
174
6.10.
Exercises
175
PART II Unconstrained Problems
Chapter
7.
Basic Properties of Solutions and Algorithms
183
7.1.
First-Order Necessary Conditions
184
7.2.
Examples of Unconstrained Problems
186
7.3.
Second-Order Conditions
190
7.4.
Convex and Concave Functions
192
7.5.
Minimization and Maximization of Convex Functions
197
7.6.
Zero-Order Conditions
198
7.7.
Global Convergence of Descent Algorithms
201
7.8.
Speed of Convergence
208
7.9.
Summary
212
7.10.
Exercises
213
Chapter
8.
Basic Descent Methods
8.1.
Fibonacci and Golden Section Search
8.2.
Line Search by Curve Fitting
8.3.
Global Convergence of Curve Fitting
8.4.
Closedness of Line Search Algorithms
8.5.
Inaccurate Line Search
8.6.
The Method of Steepest Descent
215
216
219
226
228
230
233
Contents
XI
8.7.
Applications
of the
Theory
8.8.
Newton s Method
8.9.
Coordinate Descent
Methods
8.10.
Spacer Steps
8.11.
Summary
8.12.
Exercises
242
246
253
255
256
257
Chapter
9.
Conjugate Direction Methods
263
9.1.
Conjugate Directions
263
9.2.
Descent Properties of the Conjugate Direction Method
266
9.3.
The Conjugate Gradient Method
268
9.4.
The
С
-G
Method as an Optimal Process
271
9.5.
The Partial Conjugate Gradient Method
273
9.6.
Extension to Nonquadratic Problems
277
9.7.
Parallel Tangents
279
9.8.
Exercises
282
Chapter
10.
Quasi-Newton
Methods
285
10.1.
Modified Newton Method
285
10.2.
Construction of the Inverse
288
10.3.
Davidon-Fletcher-Powell Method
290
10.4.
The Broyden Family
293
10.5.
Convergence Properties
296
10.6.
Scaling
299
10.7.
Memoryless
Quasi-Newton
Methods
304
*10.8. Combination of Steepest Descent and Newton s Method
306
10.9.
Summary
312
10.10.
Exercises
313
PART III Constrained Minimization
Chapter
11.
Constrained Minimization Conditions
321
11.1.
Constraints
321
11.2.
Tangent Plane
323
11.3.
First-Order Necessary Conditions (Equality Constraints)
326
11.4.
Examples
327
11.5.
Second-Order Conditions
333
11.6.
Eigenvalues in Tangent Subspace
335
11.7.
Sensitivity
339
11.8.
Inequality Constraints
341
11.9.
Zero-Order Conditions and
Lagrange
Multipliers
346
11.10.
Summary
353
11.11.
Exercises
354
Chapter
12.
Primal Methods
359
12.1.
Advantage of Primal Methods
359
12.2.
Feasible Direction Methods
360
12.3.
Active Set Methods
363
xii
Contents
12.4. The Gradient
Projection Method
12.5.
Convergence Rate of the Gradient Projection Method
12.6.
The Reduced Gradient Method
12.7.
Convergence Rate of the Reduced Gradient Method
12.8.
Variations
12.9.
Summary
12.10.
Exercises
367
374
382
387
394
396
396
Chapter
13.
Penalty and Barrier Methods
13.1.
Penalty Methods
13.2.
Barrier Methods
13.3.
Properties of Penalty and Barrier Functions
13.4.
Newton s Method and Penalty Functions
13.5.
Conjugate Gradients and Penalty Methods
13.6.
Normalization of Penalty Functions
13.7.
Penalty Functions and Gradient Projection
13.8.
Exact Penalty Functions
13.9.
Summary
13.10.
Exercises
401
402
405
407
416
418
420
421
425
429
430
Chapter
14.
Dual and Cutting Plane Methods
14.1.
Global Duality
14.2.
Local Duality
14.3.
Dual Canonical Convergence Rate
14.4.
Separable Problems
14.5.
Augmented Lagrangians
14.6.
The Dual Viewpoint
14.7.
Cutting Plane Methods
14.8.
Kelley s Convex Cutting Plane Algorithm
14.9.
Modifications
14.10.
Exercises
435
435
441
446
447
451
456
460
463
465
466
Chapter
15.
Primal-Dual Methods
15.1.
The Standard Problem
15.2.
Strategies
15.3.
A Simple Merit Function
15.4.
Basic Primal-Dual Methods
15.5.
Modified Newton Methods
15.6.
Descent Properties
15.7.
Rate of Convergence
15.8.
Interior Point Methods
15.9.
Semidefinite
Programming
15.10.
Summary
15.11.
Exercises
469
469
471
472
474
479
481
485
487
491
498
499
Appendix A. Mathematical Review
A.I. Sets
A.2. Matrix Notation
A.3. Spaces
507
507
508
509
Appendix
В.
Bibliography
Index
Contents
xiii
A.4.
A.5.
A.6.
Eigenvalues and Quadratic Forms
Topological Concepts
Functions
510
511
512
Convex Sets
B.I. Basic Definitions
B.2.
Hyperplanes
and Polytopes
B.3. Separating and Supporting
Hyperplanes
В
.4.
Extreme Points
515
515
517
519
521
Gaussian Elimination
523
527
541
|
| adam_txt |
CONTENTS
Chapter
1.
Introduction
1.1.
Optimization
1.2.
Types of Problems
1.3.
Size of Problems
1.4.
Iterative Algorithms and Convergence
PART I Linear Programming
Chapter
2.
Chapter
3.
Chapter
4.
Basic Properties of Linear Programs
11
2.1.
Introduction
11
2.2.
Examples of Linear Programming Problems
14
2.3.
Basic Solutions
19
2.4.
The Fundamental Theorem of Linear Programming
20
2.5.
Relations to Convexity
22
2.6.
Exercises
28
The
Simplex Method
33
3.1.
Pivots
33
3.2.
Adjacent Extreme Points
38
3.3.
Determining a Minimum Feasible Solution
42
3.4.
Computational Procedure
—
Simplex Method
46
3.5.
Artificial Variables
50
3.6.
Matrix Form of the Simplex Method
54
3.7.
The Revised Simplex Method
56
3.8.
The Simplex Method and
LU
Decomposition
59
3.9.
Decomposition
62
3.10.
Summary
70
3.11.
Exercises
70
Duality
79
4.1.
Dual Linear Programs
79
4.2.
The Duality Theorem
82
4.3.
Relations to the Siirrolex Procedure
84
4.4.
Sensitivity and Complementary Slackness
*4.5. The Dual Simplex Method
ix
90
Contents
Chapter
5.
Chapter
6.
4.6.
The Primal-Dual Algorithm
93
*4.7.
Reduction of Linear Inequalities
98
4.8.
Exercises
103
Interior-Point Methods
111
5.1.
Elements of Complexity Theory
112
*5.2.
The Simplex Method is not Polynomial-Time
114
*5.3.
The Ellipsoid Method
115
5.4.
The Analytic Center
118
5.5.
The Central Path
121
5.6.
Solution Strategies
126
5.7.
Termination and Initialization
134
5.8.
Summary
139
5.9.
Exercises
140
Transportation and Network Flow Problems
145
6.1.
The Transportation Problem
145
6.2.
Finding a Basic Feasible Solution
148
6.3.
Basis Triangularity
150
6.4.
Simplex Method for Transportation Problems
153
6.5.
The Assignment Problem
159
6.6.
Basic Network Concepts
160
6.7.
Minimum Cost Flow
162
6.8.
Maximal Flow
166
6.9.
Summary
174
6.10.
Exercises
175
PART II Unconstrained Problems
Chapter
7.
Basic Properties of Solutions and Algorithms
183
7.1.
First-Order Necessary Conditions
184
7.2.
Examples of Unconstrained Problems
186
7.3.
Second-Order Conditions
190
7.4.
Convex and Concave Functions
192
7.5.
Minimization and Maximization of Convex Functions
197
7.6.
Zero-Order Conditions
198
7.7.
Global Convergence of Descent Algorithms
201
7.8.
Speed of Convergence
208
7.9.
Summary
212
7.10.
Exercises
213
Chapter
8.
Basic Descent Methods
8.1.
Fibonacci and Golden Section Search
8.2.
Line Search by Curve Fitting
8.3.
Global Convergence of Curve Fitting
8.4.
Closedness of Line Search Algorithms
8.5.
Inaccurate Line Search
8.6.
The Method of Steepest Descent
215
216
219
226
228
230
233
Contents
XI
8.7.
Applications
of the
Theory
8.8.
Newton's Method
8.9.
Coordinate Descent
Methods
8.10.
Spacer Steps
8.11.
Summary
8.12.
Exercises
242
246
253
255
256
257
Chapter
9.
Conjugate Direction Methods
263
9.1.
Conjugate Directions
263
9.2.
Descent Properties of the Conjugate Direction Method
266
9.3.
The Conjugate Gradient Method
268
9.4.
The
С
-G
Method as an Optimal Process
271
9.5.
The Partial Conjugate Gradient Method
273
9.6.
Extension to Nonquadratic Problems
277
9.7.
Parallel Tangents
279
9.8.
Exercises
282
Chapter
10.
Quasi-Newton
Methods
285
10.1.
Modified Newton Method
285
10.2.
Construction of the Inverse
288
10.3.
Davidon-Fletcher-Powell Method
290
10.4.
The Broyden Family
293
10.5.
Convergence Properties
296
10.6.
Scaling
299
10.7.
Memoryless
Quasi-Newton
Methods
304
*10.8. Combination of Steepest Descent and Newton's Method
306
10.9.
Summary
312
10.10.
Exercises
313
PART III Constrained Minimization
Chapter
11.
Constrained Minimization Conditions
321
11.1.
Constraints
321
11.2.
Tangent Plane
323
11.3.
First-Order Necessary Conditions (Equality Constraints)
326
11.4.
Examples
327
11.5.
Second-Order Conditions
333
11.6.
Eigenvalues in Tangent Subspace
335
11.7.
Sensitivity
339
11.8.
Inequality Constraints
341
11.9.
Zero-Order Conditions and
Lagrange
Multipliers
346
11.10.
Summary
353
11.11.
Exercises
354
Chapter
12.
Primal Methods
359
12.1.
Advantage of Primal Methods
359
12.2.
Feasible Direction Methods
360
12.3.
Active Set Methods
363
xii
Contents
12.4. The Gradient
Projection Method
12.5.
Convergence Rate of the Gradient Projection Method
12.6.
The Reduced Gradient Method
12.7.
Convergence Rate of the Reduced Gradient Method
12.8.
Variations
12.9.
Summary
12.10.
Exercises
367
374
382
387
394
396
396
Chapter
13.
Penalty and Barrier Methods
13.1.
Penalty Methods
13.2.
Barrier Methods
13.3.
Properties of Penalty and Barrier Functions
13.4.
Newton's Method and Penalty Functions
13.5.
Conjugate Gradients and Penalty Methods
13.6.
Normalization of Penalty Functions
13.7.
Penalty Functions and Gradient Projection
13.8.
Exact Penalty Functions
13.9.
Summary
13.10.
Exercises
401
402
405
407
416
418
420
421
425
429
430
Chapter
14.
Dual and Cutting Plane Methods
14.1.
Global Duality
14.2.
Local Duality
14.3.
Dual Canonical Convergence Rate
14.4.
Separable Problems
14.5.
Augmented Lagrangians
14.6.
The Dual Viewpoint
14.7.
Cutting Plane Methods
14.8.
Kelley's Convex Cutting Plane Algorithm
14.9.
Modifications
14.10.
Exercises
435
435
441
446
447
451
456
460
463
465
466
Chapter
15.
Primal-Dual Methods
15.1.
The Standard Problem
15.2.
Strategies
15.3.
A Simple Merit Function
15.4.
Basic Primal-Dual Methods
15.5.
Modified Newton Methods
15.6.
Descent Properties
15.7.
Rate of Convergence
15.8.
Interior Point Methods
15.9.
Semidefinite
Programming
15.10.
Summary
15.11.
Exercises
469
469
471
472
474
479
481
485
487
491
498
499
Appendix A. Mathematical Review
A.I. Sets
A.2. Matrix Notation
A.3. Spaces
507
507
508
509
Appendix
В.
Bibliography
Index
Contents
xiii
A.4.
A.5.
A.6.
Eigenvalues and Quadratic Forms
Topological Concepts
Functions
510
511
512
Convex Sets
B.I. Basic Definitions
B.2.
Hyperplanes
and Polytopes
B.3. Separating and Supporting
Hyperplanes
В
.4.
Extreme Points
515
515
517
519
521
Gaussian Elimination
523
527
541 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Luenberger, David G. 1937- Ye, Yinyu |
| author_GND | (DE-588)135911338 |
| author_facet | Luenberger, David G. 1937- Ye, Yinyu |
| author_role | aut aut |
| author_sort | Luenberger, David G. 1937- |
| author_variant | d g l dg dgl y y yy |
| building | Verbundindex |
| bvnumber | BV022969870 |
| callnumber-first | T - Technology |
| callnumber-label | T57 |
| callnumber-raw | T57.7 |
| callnumber-search | T57.7 |
| callnumber-sort | T 257.7 |
| callnumber-subject | T - General Technology |
| classification_rvk | QH 400 QH 421 SK 870 ST 600 |
| classification_tum | MAT 910f |
| ctrlnum | (OCoLC)171549627 (DE-599)DNB985051531 |
| dewey-full | 519.72 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.72 |
| dewey-search | 519.72 |
| dewey-sort | 3519.72 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik Wirtschaftswissenschaften |
| discipline_str_mv | Informatik Mathematik Wirtschaftswissenschaften |
| edition | 3. ed. |
| format | Book |
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| id | DE-604.BV022969870 |
| illustrated | Illustrated |
| index_date | 2024-07-02T19:08:07Z |
| indexdate | 2024-07-09T21:08:50Z |
| institution | BVB |
| isbn | 9780387745022 0387745025 9780387745039 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016174131 |
| oclc_num | 171549627 |
| open_access_boolean | |
| owner | DE-703 DE-739 DE-384 DE-573 DE-634 DE-20 DE-91G DE-BY-TUM DE-11 DE-355 DE-BY-UBR DE-29T DE-706 DE-859 DE-83 |
| owner_facet | DE-703 DE-739 DE-384 DE-573 DE-634 DE-20 DE-91G DE-BY-TUM DE-11 DE-355 DE-BY-UBR DE-29T DE-706 DE-859 DE-83 |
| physical | XIII, 546 S. Ill., graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Springer |
| record_format | marc |
| series | International series in operations research & management science |
| series2 | International series in operations research & management science |
| spelling | Luenberger, David G. 1937- Verfasser (DE-588)135911338 aut Linear and nonlinear programming David G. Luenberger ; Yinyu Ye 3. ed. New York, NY Springer 2008 XIII, 546 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier International series in operations research & management science 116 Auch als Internetausgabe Linear programming Nonlinear programming Optimierung (DE-588)4043664-0 gnd rswk-swf Lineare Optimierung (DE-588)4035816-1 gnd rswk-swf Lineare Ordnung (DE-588)4167706-7 gnd rswk-swf Nichtlineare Optimierung (DE-588)4128192-5 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 Ye, Yinyu Verfasser aut International series in operations research & management science 116 (DE-604)BV011630976 116 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016174131&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. 1937- Ye, Yinyu Linear and nonlinear programming International series in operations research & management science Linear programming Nonlinear programming Optimierung (DE-588)4043664-0 gnd Lineare Optimierung (DE-588)4035816-1 gnd Lineare Ordnung (DE-588)4167706-7 gnd Nichtlineare Optimierung (DE-588)4128192-5 gnd |
| subject_GND | (DE-588)4043664-0 (DE-588)4035816-1 (DE-588)4167706-7 (DE-588)4128192-5 |
| 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 ; Yinyu Ye |
| title_fullStr | Linear and nonlinear programming David G. Luenberger ; Yinyu Ye |
| title_full_unstemmed | Linear and nonlinear programming David G. Luenberger ; Yinyu Ye |
| title_short | Linear and nonlinear programming |
| title_sort | linear and nonlinear programming |
| topic | Linear programming Nonlinear programming Optimierung (DE-588)4043664-0 gnd Lineare Optimierung (DE-588)4035816-1 gnd Lineare Ordnung (DE-588)4167706-7 gnd Nichtlineare Optimierung (DE-588)4128192-5 gnd |
| topic_facet | Linear programming Nonlinear programming Optimierung Lineare Optimierung Lineare Ordnung Nichtlineare Optimierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016174131&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV011630976 |
| work_keys_str_mv | AT luenbergerdavidg linearandnonlinearprogramming AT yeyinyu linearandnonlinearprogramming |