Linear programming with MATLAB:
This textbook provides a self-contained introduction to linear programming using MATLAB software to elucidate the development of algorithms and theory. Early chapters cover linear algebra basics, the simplex method, duality, the solving of large linear problems, sensitivity analysis, and parametric...
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Philadelphia, PA
Society for Industrial and Applied Mathematics
2007
|
| Schriftenreihe: | MOS-SIAM series on optimization
7 |
| Schlagworte: | |
| Online-Zugang: | Beschreibung für Leser Inhaltsverzeichnis Inhaltsverzeichnis |
| Zusammenfassung: | This textbook provides a self-contained introduction to linear programming using MATLAB software to elucidate the development of algorithms and theory. Early chapters cover linear algebra basics, the simplex method, duality, the solving of large linear problems, sensitivity analysis, and parametric linear programming. In later chapters, the authors discuss quadratic programming, linear complementarity, interior-point methods, and selected applications of linear programming to approximation and classification problems. Exercises are interwoven with the theory presented in each chapter, and two appendices provide additional information on linear algebra, convexity, nonlinear functions, and on available MATLAB commands, respectively. Readers can access MATLAB codes and associated mex files at a Web site maintained by the authors. Only a basic knowledge of linear algebra and calculus is required to understand this textbook, which is geared toward junior and senior-level undergraduate students, first-year graduate students, and researchers unfamiliar with linear programming. |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XI, 266 S. Ill., graph. Darst. |
| ISBN: | 9780898716436 |
Internformat
MARC
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| 084 | |a MAT 912f |2 stub | ||
| 100 | 1 | |a Ferris, Michael C. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Linear programming with MATLAB |c Michael C. Ferris ; Olvi L. Mangasarian ; Stephen J. Wright |
| 264 | 1 | |a Philadelphia, PA |b Society for Industrial and Applied Mathematics |c 2007 | |
| 300 | |a XI, 266 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a MOS-SIAM series on optimization |v 7 | |
| 500 | |a Includes bibliographical references and index | ||
| 520 | 3 | |a This textbook provides a self-contained introduction to linear programming using MATLAB software to elucidate the development of algorithms and theory. Early chapters cover linear algebra basics, the simplex method, duality, the solving of large linear problems, sensitivity analysis, and parametric linear programming. In later chapters, the authors discuss quadratic programming, linear complementarity, interior-point methods, and selected applications of linear programming to approximation and classification problems. Exercises are interwoven with the theory presented in each chapter, and two appendices provide additional information on linear algebra, convexity, nonlinear functions, and on available MATLAB commands, respectively. Readers can access MATLAB codes and associated mex files at a Web site maintained by the authors. Only a basic knowledge of linear algebra and calculus is required to understand this textbook, which is geared toward junior and senior-level undergraduate students, first-year graduate students, and researchers unfamiliar with linear programming. | |
| 630 | 0 | 4 | |a MATLAB |
| 650 | 4 | |a Datenverarbeitung | |
| 650 | 4 | |a Linear programming |x Data processing | |
| 650 | 4 | |a Mathematical optimization | |
| 650 | 4 | |a Algebras, Linear | |
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| 689 | 0 | 1 | |a Lineare Optimierung |0 (DE-588)4035816-1 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Mangasarian, Olvi L. |d 1934-2020 |e Verfasser |0 (DE-588)136623077 |4 aut | |
| 700 | 1 | |a Wright, Stephen J. |d 1960- |e Verfasser |0 (DE-588)121513300 |4 aut | |
| 830 | 0 | |a MOS-SIAM series on optimization |v 7 |w (DE-604)BV039542569 |9 7 | |
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Datensatz im Suchindex
| _version_ | 1804137180082208768 |
|---|---|
| adam_text | Contents
Preface
xi
1
Introduction
1
1.1
An Example: The Professor s Dairy
................... 2
1.1.1
The Setup
......................... 2
1.1.2
Formulating the Problem and a Graphical Solution
.... 2
1.1.3
Changing the Problem
................... 4
1.1.4
Discussion
......................... 6
1.2
Formulations
............................... 7
1.3
Applications
............................... 8
1.3.1
The Diet Problem
..................... 8
1.3.2
Linear Surface Fitting
................... 9
1.3.3
Load Balancing Problem
.................. 10
1.3.4
Resource Allocation
.................... 10
1.3.5
Classification
........................ 11
1.3.6
Minimum-Cost Network Flow
............... 12
1.4
Algorithms and Complexity
....................... 14
1.4.1
The Simplex Method
.................... 14
1.4.2
Interior-Point Methods
................... 15
2
Linear Algebra: A Constructive Approach
17
2.1
Jordan Exchange
............................. 17
2.2
Linear Independence
........................... 23
2.3
Matrix Inversion
............................. 27
2.4
Exact Solution of
m
Equations in
η
Unknowns
............. 32
2.5
Solving Linear Equations Efficiently
.................. 39
2.6
LU
Decomposition
........................... 41
3
The Simplex Method
45
3.1
A Simple Example
............................ 46
3.2
Vertices
.................................. 51
3.3
The Phase II Procedure
......................... 53
3.4
The Phase I Procedure
.......................... 60
3.5
Finite Termination
............................ 65
vii
viii Contents
3.5.1
The
Nondegenerate Case
................. 65
3.5.2
Cycling
........................... 66
3.5.3
The General Case
..................... 67
3.6
Linear Programs in
Nonstandard
Form
................ . 72
3.6.1
Transforming Constraints and Variables
.......... 72
3.6.2 Schemel.......................... 76
3.6.3 Schemen ......................... 80
3.6.4
Summary
.......................... 86
4
Duality
89
4.1
Duality and Rank in Linear Systems
.................. 89
4.2
Duality in Linear Programming
..................... 94
4.3
Interpretation of Linear Programming Duality
............. 96
4.4
Duality Theory
.............................. 97
4.5
KKT Optimality Conditions
....................... 100
4.6
Dual Simplex Method
.......................... 102
4.7
General Linear Programs
........................ 107
4.8
Big
M
Method
.............................. 110
4.9
Applications of Duality
......................... 112
5
Solving Large Linear Programs
117
5.1
Foundations
...............................118
5.1.1
Basic Feasible Solutions and Basis Matrices
.......118
5.1.2
Geometric Viewpoint
...................121
5.2
The Revised Simplex Method
......................123
5.2.1
Upper and Lower Bounds
.................129
5.2.2
Generating Basic Feasible Solutions
...........134
5.2.3
Basis Updates
.......................139
5.2.4
Advanced Pivot Selection Mechanisms
..........142
5.3
Network Flow Problems
.........................143
5.3.1
Minimum-Cost Network Flow
...............144
5.3.2
Shortest-Path Problem
...................145
5.3.3
Max-Flow Problem
....................146
5.3.4
Transportation Problem
..................147
5.3.5
Assignment Problem
....................149
5.3.6
Network Simplex Method
.................149
6
Sensitivity and Parametric Linear Programming
151
6.1
Sensitivity Analysis
...........................151
6.2
Adding New Variables or Constraints
..................155
6.3
Parametric Optimization of the Objective Function
...........158
6.4
Parametric Optimization of the Right-Hand Side
............164
7
Quadratic Programming and Complementarity Problems
169
7.1
Nonlinear Programs: Optimality Conditions
..............169
7.2
Quadratic Programming
.........................172
Contents ix
7.2.1 Basic
Existence
Result
...................172
7.2.2
ККТ
Conditions
......................173
7.2.3
Duality
...........................176
7.3
Linear Complementarity Problems
...................177
7.4
Lemke s Method
.............................178
7.5
Bimatrix Games
.............................185
7.5.1
Computing Nash Equilibria
................186
7.5.2
Zero-Sum Games As Dual Linear Programs
.......192
8
Interior-Point Methods
195
8.1
Motivation and Outline
.........................195
8.2
Newton s Method
............................197
8.3
Primal-Dual Methods
..........................201
8.3.1
An Affine-Scaling Approach
................202
8.3.2
Path-Following Methods
..................204
8.3.3
Solution of the Linear System at Each Interior-Point
Iteration
..........................208
8.3.4
Practical Primal-Dual Methods
..............209
8.4
Interior-Point vs. Simplex
........................212
8.5
Extension to Quadratic Programming
..................212
9
Approximation and Classification
217
9.1
Minimax Problems
............................217
9.2
Approximation
..............................218
9.2.1
Chebyshev Approximation
.................219
9.2.2
L,
Approximation
.....................221
9.2.3
Approximate Solutions to Systems with Inequality
Constraints
.........................223
9.2.4
Least-Squares Problems
..................224
9.3
Huber Estimation
............................227
9.4
Classification Problems
.........................230
A Linear Algebra, Convexity, and Nonlinear Functions
237
A.I Linear Algebra
..............................237
A.2 Convex Sets
...............................239
A.3 Smooth Functions
............................242
A.4 Convex Functions
............................242
A.
5
Quadratic Functions
...........................244
A.
6
Norms and Order Notation
.......................247
A.7 Taylor s Theorem
............................249
В
Summary of Available
MATLAB
Commands
251
B.I Basic
MATLAB
Operations
.......................251
B.2
MATLAB
Functions Defined in This Book
...............252
Contents
Bibliography
257
Index 261
|
| adam_txt |
Contents
Preface
xi
1
Introduction
1
1.1
An Example: The Professor's Dairy
. 2
1.1.1
The Setup
. 2
1.1.2
Formulating the Problem and a Graphical Solution
. 2
1.1.3
Changing the Problem
. 4
1.1.4
Discussion
. 6
1.2
Formulations
. 7
1.3
Applications
. 8
1.3.1
The Diet Problem
. 8
1.3.2
Linear Surface Fitting
. 9
1.3.3
Load Balancing Problem
. 10
1.3.4
Resource Allocation
. 10
1.3.5
Classification
. 11
1.3.6
Minimum-Cost Network Flow
. 12
1.4
Algorithms and Complexity
. 14
1.4.1
The Simplex Method
. 14
1.4.2
Interior-Point Methods
. 15
2
Linear Algebra: A Constructive Approach
17
2.1
Jordan Exchange
. 17
2.2
Linear Independence
. 23
2.3
Matrix Inversion
. 27
2.4
Exact Solution of
m
Equations in
η
Unknowns
. 32
2.5
Solving Linear Equations Efficiently
. 39
2.6
LU
Decomposition
. 41
3
The Simplex Method
45
3.1
A Simple Example
. 46
3.2
Vertices
. 51
3.3
The Phase II Procedure
. 53
3.4
The Phase I Procedure
. 60
3.5
Finite Termination
. 65
vii
viii Contents
3.5.1
The
Nondegenerate Case
. 65
3.5.2
Cycling
. 66
3.5.3
The General Case
. 67
3.6
Linear Programs in
Nonstandard
Form
. . 72
3.6.1
Transforming Constraints and Variables
. 72
3.6.2 Schemel. 76
3.6.3 Schemen . 80
3.6.4
Summary
. 86
4
Duality
89
4.1
Duality and Rank in Linear Systems
. 89
4.2
Duality in Linear Programming
. 94
4.3
Interpretation of Linear Programming Duality
. 96
4.4
Duality Theory
. 97
4.5
KKT Optimality Conditions
. 100
4.6
Dual Simplex Method
. 102
4.7
General Linear Programs
. 107
4.8
Big
M
Method
. 110
4.9
Applications of Duality
. 112
5
Solving Large Linear Programs
117
5.1
Foundations
.118
5.1.1
Basic Feasible Solutions and Basis Matrices
.118
5.1.2
Geometric Viewpoint
.121
5.2
The Revised Simplex Method
.123
5.2.1
Upper and Lower Bounds
.129
5.2.2
Generating Basic Feasible Solutions
.134
5.2.3
Basis Updates
.139
5.2.4
Advanced Pivot Selection Mechanisms
.142
5.3
Network Flow Problems
.143
5.3.1
Minimum-Cost Network Flow
.144
5.3.2
Shortest-Path Problem
.145
5.3.3
Max-Flow Problem
.146
5.3.4
Transportation Problem
.147
5.3.5
Assignment Problem
.149
5.3.6
Network Simplex Method
.149
6
Sensitivity and Parametric Linear Programming
151
6.1
Sensitivity Analysis
.151
6.2
Adding New Variables or Constraints
.155
6.3
Parametric Optimization of the Objective Function
.158
6.4
Parametric Optimization of the Right-Hand Side
.164
7
Quadratic Programming and Complementarity Problems
169
7.1
Nonlinear Programs: Optimality Conditions
.169
7.2
Quadratic Programming
.172
Contents ix
7.2.1 Basic
Existence
Result
.172
7.2.2
ККТ
Conditions
.173
7.2.3
Duality
.176
7.3
Linear Complementarity Problems
.177
7.4
Lemke's Method
.178
7.5
Bimatrix Games
.185
7.5.1
Computing Nash Equilibria
.186
7.5.2
Zero-Sum Games As Dual Linear Programs
.192
8
Interior-Point Methods
195
8.1
Motivation and Outline
.195
8.2
Newton's Method
.197
8.3
Primal-Dual Methods
.201
8.3.1
An Affine-Scaling Approach
.202
8.3.2
Path-Following Methods
.204
8.3.3
Solution of the Linear System at Each Interior-Point
Iteration
.208
8.3.4
Practical Primal-Dual Methods
.209
8.4
Interior-Point vs. Simplex
.212
8.5
Extension to Quadratic Programming
.212
9
Approximation and Classification
217
9.1
Minimax Problems
.217
9.2
Approximation
.218
9.2.1
Chebyshev Approximation
.219
9.2.2
L,
Approximation
.221
9.2.3
Approximate Solutions to Systems with Inequality
Constraints
.223
9.2.4
Least-Squares Problems
.224
9.3
Huber Estimation
.227
9.4
Classification Problems
.230
A Linear Algebra, Convexity, and Nonlinear Functions
237
A.I Linear Algebra
.237
A.2 Convex Sets
.239
A.3 Smooth Functions
.242
A.4 Convex Functions
.242
A.
5
Quadratic Functions
.244
A.
6
Norms and Order Notation
.247
A.7 Taylor's Theorem
.249
В
Summary of Available
MATLAB
Commands
251
B.I Basic
MATLAB
Operations
.251
B.2
MATLAB
Functions Defined in This Book
.252
Contents
Bibliography
257
Index 261 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Ferris, Michael C. Mangasarian, Olvi L. 1934-2020 Wright, Stephen J. 1960- |
| author_GND | (DE-588)136623077 (DE-588)121513300 |
| author_facet | Ferris, Michael C. Mangasarian, Olvi L. 1934-2020 Wright, Stephen J. 1960- |
| author_role | aut aut aut |
| author_sort | Ferris, Michael C. |
| author_variant | m c f mc mcf o l m ol olm s j w sj sjw |
| building | Verbundindex |
| bvnumber | BV022942188 |
| callnumber-first | Q - Science |
| callnumber-label | QA402 |
| callnumber-raw | QA402.5 |
| callnumber-search | QA402.5 |
| callnumber-sort | QA 3402.5 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 870 ST 601 |
| classification_tum | DAT 306f MAT 912f |
| ctrlnum | (OCoLC)156892047 (DE-599)BVBBV022942188 |
| 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 | Informatik Mathematik |
| discipline_str_mv | Informatik Mathematik |
| format | Book |
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Ferris ; Olvi L. Mangasarian ; Stephen J. Wright</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Philadelphia, PA</subfield><subfield code="b">Society for Industrial and Applied Mathematics</subfield><subfield code="c">2007</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XI, 266 S.</subfield><subfield code="b">Ill., graph. 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Early chapters cover linear algebra basics, the simplex method, duality, the solving of large linear problems, sensitivity analysis, and parametric linear programming. In later chapters, the authors discuss quadratic programming, linear complementarity, interior-point methods, and selected applications of linear programming to approximation and classification problems. Exercises are interwoven with the theory presented in each chapter, and two appendices provide additional information on linear algebra, convexity, nonlinear functions, and on available MATLAB commands, respectively. Readers can access MATLAB codes and associated mex files at a Web site maintained by the authors. 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| id | DE-604.BV022942188 |
| illustrated | Illustrated |
| index_date | 2024-07-02T18:58:27Z |
| indexdate | 2024-07-09T21:08:11Z |
| institution | BVB |
| isbn | 9780898716436 |
| language | English |
| lccn | 2007061748 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016146817 |
| oclc_num | 156892047 |
| open_access_boolean | |
| owner | DE-20 DE-703 DE-91G DE-BY-TUM DE-634 DE-859 DE-384 |
| owner_facet | DE-20 DE-703 DE-91G DE-BY-TUM DE-634 DE-859 DE-384 |
| physical | XI, 266 S. Ill., graph. Darst. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Society for Industrial and Applied Mathematics |
| record_format | marc |
| series | MOS-SIAM series on optimization |
| series2 | MOS-SIAM series on optimization |
| spelling | Ferris, Michael C. Verfasser aut Linear programming with MATLAB Michael C. Ferris ; Olvi L. Mangasarian ; Stephen J. Wright Philadelphia, PA Society for Industrial and Applied Mathematics 2007 XI, 266 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier MOS-SIAM series on optimization 7 Includes bibliographical references and index This textbook provides a self-contained introduction to linear programming using MATLAB software to elucidate the development of algorithms and theory. Early chapters cover linear algebra basics, the simplex method, duality, the solving of large linear problems, sensitivity analysis, and parametric linear programming. In later chapters, the authors discuss quadratic programming, linear complementarity, interior-point methods, and selected applications of linear programming to approximation and classification problems. Exercises are interwoven with the theory presented in each chapter, and two appendices provide additional information on linear algebra, convexity, nonlinear functions, and on available MATLAB commands, respectively. Readers can access MATLAB codes and associated mex files at a Web site maintained by the authors. Only a basic knowledge of linear algebra and calculus is required to understand this textbook, which is geared toward junior and senior-level undergraduate students, first-year graduate students, and researchers unfamiliar with linear programming. MATLAB Datenverarbeitung Linear programming Data processing Mathematical optimization Algebras, Linear Lineare Optimierung (DE-588)4035816-1 gnd rswk-swf MATLAB (DE-588)4329066-8 gnd rswk-swf MATLAB (DE-588)4329066-8 s Lineare Optimierung (DE-588)4035816-1 s DE-604 Mangasarian, Olvi L. 1934-2020 Verfasser (DE-588)136623077 aut Wright, Stephen J. 1960- Verfasser (DE-588)121513300 aut MOS-SIAM series on optimization 7 (DE-604)BV039542569 7 http://catdir.loc.gov/catdir/enhancements/fy0805/2007061748-d.html Beschreibung für Leser http://catdir.loc.gov/catdir/enhancements/fy0805/2007061748-t.html Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016146817&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ferris, Michael C. Mangasarian, Olvi L. 1934-2020 Wright, Stephen J. 1960- Linear programming with MATLAB MOS-SIAM series on optimization MATLAB Datenverarbeitung Linear programming Data processing Mathematical optimization Algebras, Linear Lineare Optimierung (DE-588)4035816-1 gnd MATLAB (DE-588)4329066-8 gnd |
| subject_GND | (DE-588)4035816-1 (DE-588)4329066-8 |
| title | Linear programming with MATLAB |
| title_auth | Linear programming with MATLAB |
| title_exact_search | Linear programming with MATLAB |
| title_exact_search_txtP | Linear programming with MATLAB |
| title_full | Linear programming with MATLAB Michael C. Ferris ; Olvi L. Mangasarian ; Stephen J. Wright |
| title_fullStr | Linear programming with MATLAB Michael C. Ferris ; Olvi L. Mangasarian ; Stephen J. Wright |
| title_full_unstemmed | Linear programming with MATLAB Michael C. Ferris ; Olvi L. Mangasarian ; Stephen J. Wright |
| title_short | Linear programming with MATLAB |
| title_sort | linear programming with matlab |
| topic | MATLAB Datenverarbeitung Linear programming Data processing Mathematical optimization Algebras, Linear Lineare Optimierung (DE-588)4035816-1 gnd MATLAB (DE-588)4329066-8 gnd |
| topic_facet | MATLAB Datenverarbeitung Linear programming Data processing Mathematical optimization Algebras, Linear Lineare Optimierung |
| url | http://catdir.loc.gov/catdir/enhancements/fy0805/2007061748-d.html http://catdir.loc.gov/catdir/enhancements/fy0805/2007061748-t.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016146817&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV039542569 |
| work_keys_str_mv | AT ferrismichaelc linearprogrammingwithmatlab AT mangasarianolvil linearprogrammingwithmatlab AT wrightstephenj linearprogrammingwithmatlab |
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