Linear and nonlinear optimization:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Philadelphia
SIAM
2009
|
| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XXII, 742 S. Ill., graph. Darst. |
| ISBN: | 9780898716610 |
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MARC
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| 100 | 1 | |a Griva, Igor |e Verfasser |0 (DE-588)137672012 |4 aut | |
| 245 | 1 | 0 | |a Linear and nonlinear optimization |c Igor Griva ; Stephen G. Nash ; Ariela Sofer |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Philadelphia |b SIAM |c 2009 | |
| 300 | |a XXII, 742 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Linear programming | |
| 650 | 4 | |a Nonlinear programming | |
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| 700 | 1 | |a Nash, Stephen G. |e Verfasser |0 (DE-588)128553634 |4 aut | |
| 700 | 1 | |a Sofer, Ariela |e Verfasser |0 (DE-588)138320195 |4 aut | |
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| _version_ | 1804138094124859392 |
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| adam_text | Titel: Linear and nonlinear optimization
Autor: Griva, Igor
Jahr: 2009
Contents
Preface xiii
I Basics 1
1 Optimization Models 3
1.1 Introduction............................... 3
1.2 Optimization: An Informal Introduction................ 4
1.3 Linear Equations............................. 7
1.4 Linear Optimization........................... 10
Exercises..................................... 12
1.5 Least-Squares Data Fitting ....................... 12
Exercises..................................... 14
1.6 Nonlinear Optimization......................... 14
1.7 Optimization Applications........................ 18
1.7.1 Crew Scheduling and Fleet Scheduling.......... 18
Exercises..................................... 22
1.7.2 Support Vector Machines................. 22
Exercises..................................... 24
1.7.3 Portfolio Optimization................... 25
Exercises..................................... 27
1.7.4 Intensity Modulated Radiation Treatment Planning . ... 28
Exercises..................................... 31
1.7.5 Positron Emission Tomography Image Reconstruction . . 32
Exercises..................................... 34
1.7.6 Shape Optimization.................... 35
1.8 Notes................................... 40
2 Fundamentals of Optimization 43
2.1 Introduction............................... 43
2.2 Feasibility and Optimality........................ 43
Exercises..................................... 47
2.3 Convexity................................ 48
2.3.1 Derivatives and Convexity................. 50
vi Contents
Exercises..................................... 52
2.4 The General Optimization Algorithm.................. 54
Exercises..................................... 58
2.5 Rates of Convergence.......................... 58
Exercises..................................... 61
2.6 Taylor Series............................... 62
Exercises..................................... 65
2.7 Newton s Method for Nonlinear Equations............... 67
2.7.1 Systems of Nonlinear Equations.............. 72
Exercises..................................... 74
2.8 Notes................................... 76
3 Representation of Linear Constraints 77
3.1 Basic Concepts.............................. 77
Exercises..................................... 82
3.2 Null and Range Spaces ......................... 82
Exercises..................................... 84
3.3 Generating Null-Space Matrices..................... 86
3.3.1 Variable Reduction Method................ 86
3.3.2 Orthogonal Projection Matrix............... 89
3.3.3 Other Projections ..................... 90
3.3.4 The QR Factorization................... 90
Exercises..................................... 91
3.4 Notes................................... 93
II Linear Programming 95
4 Geometry of Linear Programming 97
4.1 Introduction...............................97
Exercises.....................................98
4.2 Standard Form..............................100
Exercises.....................................105
4.3 Basic Solutions and Extreme Points...................106
Exercises.....................................114
4.4 Representation of Solutions; Optimality ................117
Exercises.....................................123
4.5 Notes...................................124
5 The Simplex Method 125
5.1 Introduction...............................125
5.2 The Simplex Method ..........................126
5.2.1 General Formulas.....................129
5.2.2 Unbounded Problems...................134
5.2.3 Notation for the Simplex Method (Tableaus).......135
5.2.4 Deficiencies of the Tableau................139
Contents vü
Exercises.....................................141
5.3 The Simplex Method (Details) .....................144
5.3.1 Multiple Solutions.....................144
5.3.2 Feasible Directions and Edge Directions.........145
Exercises.....................................148
5.4 Getting Started—Artificial Variables..................149
5.4.1 The Two-Phase Method.................. 150
5.4.2 The Big-M Method .................... 156
Exercises..................................... 159
5.5 Degeneracy and Termination ...................... 162
5.5.1 Resolving Degeneracy Using Perturbation........ 167
Exercises.....................................170
5.6 Notes...................................171
6 Duality and Sensitivity 173
6.1 The Dual Problem............................173
Exercises.....................................177
6.2 Duality Theory..............................179
6.2.1 Complementary Slackness.................182
6.2.2 Interpretation of the Dual.................184
Exercises.....................................185
6.3 The Dual Simplex Method........................189
Exercises.....................................194
6.4 Sensitivity................................195
Exercises.....................................201
6.5 Parametric Linear Programming.....................204
Exercises.....................................210
6.6 Notes...................................211
7 Enhancements of the Simplex Method 213
7.1 Introduction...............................213
7.2 Problems with Upper Bounds......................214
Exercises.....................................221
7.3 Column Generation...........................222
Exercises.....................................227
7.4 The Decomposition Principle......................227
Exercises.....................................238
7.5 Representation of the Basis.......................240
7.5.1 The Product Form of the Inverse .............240
7.5.2 Representation of the Basis—The LU Factorization ...248
Exercises.....................................256
7.6 Numerical Stability and Computational Efficiency...........259
7.6.1 Pricing...........................260
7.6.2 The Initial Basis......................264
7.6.3 Tolerances; Degeneracy..................265
7.6.4 Scaling...........................266
viii Contents
7.6.5 Preprocessing.......................267
7.6.6 Model Formats.......................268
Exercises.....................................269
7.7 Notes...................................270
8 Network Problems 271
8.1 Introduction...............................271
8.2 Basic Concepts and Examples......................271
Exercises.....................................280
8.3 Representation of the Basis.......................280
Exercises.....................................287
8.4 The Network Simplex Method .....................287
Exercises.....................................294
8.5 Resolving Degeneracy..........................295
Exercises.....................................299
8.6 Notes...................................299
9 Computational Complexity of Linear Programming 301
9.1 Introduction...............................301
9.2 Computational Complexity.......................302
Exercises.....................................304
9.3 Worst-Case Behavior of the Simplex Method..............305
Exercises.....................................308
9.4 The Ellipsoid Method..........................308
Exercises.....................................313
9.5 The Average-Case Behavior of the Simplex Method..........314
9.6 Notes...................................316
10 Interior-Point Methods for Linear Programming 319
10.1 Introduction...............................319
10.2 The Primal-Dual Interior-Point Method.................321
10.2.1 Computational Aspects of Interior-Point Methods . . . .328
10.2.2 The Predictor-Corrector Algorithm............329
Exercises.....................................330
10.3 Feasibility and Self-Dual Formulations.................331
Exercises.....................................334
10.4 Some Concepts from Nonlinear Optimization .............334
10.5 Affine-Scaling Methods.........................336
Exercises.....................................343
10.6 Path-Following Methods ........................344
Exercises.....................................352
10.7 Notes...................................353
Contents ¡x
III Unconstrained Optimization 355
11 Basics of Unconstrained Optimization 357
11.1 Introduction...............................357
11.2 Optimality Conditions..........................357
Exercises.....................................361
11.3 Newton s Method for Minimization...................364
Exercises.....................................369
11.4 Guaranteeing Descent..........................371
Exercises.....................................374
11.5 Guaranteeing Convergence: Line Search Methods...........375
11.5.1 Other Line Searches....................381
Exercises.....................................385
11.6 Guaranteeing Convergence: Trust-Region Methods..........391
Exercises.....................................398
11.7 Notes...................................399
12 Methods for Unconstrained Optimization 401
12.1 Introduction...............................401
12.2 Steepest-Descent Method........................402
Exercises.....................................408
12.3 Quasi-Newton Methods.........................411
Exercises.....................................420
12.4 Automating Derivative Calculations...................422
12.4.1 Finite-Difference Derivative Estimates..........422
12.4.2 Automatic Differentiation.................426
Exercises.....................................429
12.5 Methods That Do Not Require Derivatives...............431
12.5.1 Simulation-Based Optimization..............432
12.5.2 Compass Search: A Derivative-Free Method.......434
12.5.3 Convergence of Compass Search.............437
Exercises.....................................440
12.6 Termination Rules............................441
Exercises.....................................445
12.7 Historical Background..........................446
12.8 Notes...................................448
13 Low-Storage Methods for Unconstrained Problems 451
13.1 Introduction...............................451
13.2 The Conjugate-Gradient Method for Solving Linear Equations . . . .452
Exercises.....................................459
13.3 Truncated-Newton Methods.......................460
Exercises.....................................465
13.4 Nonlinear Conjugate-Gradient Methods.................466
Exercises.....................................469
13.5 Limited-Memory Quasi-Newton Methods ...............470
Contents
Exercises.....................................473
13.6 Preconditioning.............................474
Exercises.....................................477
13.7 Notes...................................478
IV Nonlinear Optimization 481
14 Optimality Conditions for Constrained Problems 483
14.1 Introduction...............................483
14.2 Optimality Conditions for Linear Equality Constraints.........484
Exercises.....................................489
14.3 The Lagrange Multipliers and the Lagrangian Function ........491
Exercises.....................................493
14.4 Optimality Conditions for Linear Inequality Constraints........494
Exercises.....................................501
14.5 Optimality Conditions for Nonlinear Constraints............502
14.5.1 Statement of Optimality Conditions............503
Exercises.....................................508
14.6 Preview of Methods...........................510
Exercises.....................................514
14.7 Derivation of Optimality Conditions for Nonlinear Constraints . . . .515
Exercises.....................................520
14.8 Duality..................................522
14.8.1 Games and Min-Max Duality...............523
14.8.2 Lagrangian Duality ....................526
14.8.3 Wolfe Duality.......................532
14.8.4 More on the Dual Function................534
14.8.5 Duality in Support Vector Machines............538
Exercises.....................................542
14.9 Historical Background..........................543
14.10 Notes...................................546
15 Feasible-Point Methods 549
15.1 Introduction...............................549
15.2 Linear Equality Constraints.......................549
Exercises.....................................555
15.3 Computing the Lagrange Multipliers..................556
Exercises.....................................561
15.4 Linear Inequality Constraints......................563
15.4.1 Linear Programming....................570
Exercises.....................................572
15.5 Sequential Quadratic Programming...................573
Exercises.....................................580
15.6 Reduced-Gradient Methods.......................581
Exercises.....................................588
Contents x¡
15.7 Filter Methods..............................588
Exercises.....................................597
15.8 Notes...................................598
16 Penalty and Barrier Methods 601
16.1 Introduction...............................601
16.2 Classical Penalty and Barrier Methods.................602
16.2.1 Barrier Methods......................603
16.2.2 Penalty Methods......................610
16.2.3 Convergence........................613
Exercises.....................................617
16.3 Ill-Conditioning.............................618
16.4 Stabilized Penalty and Barrier Methods.................619
Exercises.....................................623
16.5 Exact Penalty Methods .........................623
Exercises.....................................626
16.6 Multiplier-Based Methods........................626
16.6.1 Dual Interpretation.....................635
Exercises.....................................638
16.7 Nonlinear Primal-Dual Methods.....................640
16.7.1 Primal-Dual Interior-Point Methods............641
16.7.2 Convergence of the Primal-Dual Interior-Point Method .645
Exercises.....................................647
16.8 Semidefinite Programming .......................649
Exercises.....................................654
16.9 Notes...................................656
V Appendices 659
A Topics from Linear Algebra 661
A.I Introduction...............................661
A.2 Eigenvalues...............................661
A.3 Vector and Matrix Norms........................662
A.4 Systems of Linear Equations ......................664
A.5 Solving Systems of Linear Equations by Elimination..........666
A.6 Gaussian Elimination as a Matrix Factorization.............669
A.6.1 Sparse Matrix Storage...................675
A.7 Other Matrix Factorizations.......................676
A.7.1 Positive-Definite Matrices.................677
A.7.2 The LDLT and Cholesky Factorizations..........678
A.7.3 An Orthogonal Matrix Factorization............681
A.8 Sensitivity (Conditioning)........................683
A.9 The Sherman-Morrison Formula....................686
A.10 Notes...................................688
xü Contents
B Other Fundamentals 691
B.I Introduction...............................691
B.2 Computer Arithmetic ..........................691
B.3 Big-0 Notation, O(-) ..........................693
B.4 The Gradient, Hessian, and Jacobian..................694
B.5 Gradient and Hessian of a Quadratic Function.............696
B.6 Derivatives of a Product.........................697
B.7 The Chain Rule.............................698
B.8 Continuous Functions; Closed and Bounded Sets............699
B.9 The Implicit Function Theorem.....................700
C Software 703
C.I Software.................................703
Bibliography 707
Index 727
|
| adam_txt |
Titel: Linear and nonlinear optimization
Autor: Griva, Igor
Jahr: 2009
Contents
Preface xiii
I Basics 1
1 Optimization Models 3
1.1 Introduction. 3
1.2 Optimization: An Informal Introduction. 4
1.3 Linear Equations. 7
1.4 Linear Optimization. 10
Exercises. 12
1.5 Least-Squares Data Fitting . 12
Exercises. 14
1.6 Nonlinear Optimization. 14
1.7 Optimization Applications. 18
1.7.1 Crew Scheduling and Fleet Scheduling. 18
Exercises. 22
1.7.2 Support Vector Machines. 22
Exercises. 24
1.7.3 Portfolio Optimization. 25
Exercises. 27
1.7.4 Intensity Modulated Radiation Treatment Planning . . 28
Exercises. 31
1.7.5 Positron Emission Tomography Image Reconstruction . . 32
Exercises. 34
1.7.6 Shape Optimization. 35
1.8 Notes. 40
2 Fundamentals of Optimization 43
2.1 Introduction. 43
2.2 Feasibility and Optimality. 43
Exercises. 47
2.3 Convexity. 48
2.3.1 Derivatives and Convexity. 50
vi Contents
Exercises. 52
2.4 The General Optimization Algorithm. 54
Exercises. 58
2.5 Rates of Convergence. 58
Exercises. 61
2.6 Taylor Series. 62
Exercises. 65
2.7 Newton's Method for Nonlinear Equations. 67
2.7.1 Systems of Nonlinear Equations. 72
Exercises. 74
2.8 Notes. 76
3 Representation of Linear Constraints 77
3.1 Basic Concepts. 77
Exercises. 82
3.2 Null and Range Spaces . 82
Exercises. 84
3.3 Generating Null-Space Matrices. 86
3.3.1 Variable Reduction Method. 86
3.3.2 Orthogonal Projection Matrix. 89
3.3.3 Other Projections . 90
3.3.4 The QR Factorization. 90
Exercises. 91
3.4 Notes. 93
II Linear Programming 95
4 Geometry of Linear Programming 97
4.1 Introduction.97
Exercises.98
4.2 Standard Form.100
Exercises.105
4.3 Basic Solutions and Extreme Points.106
Exercises.114
4.4 Representation of Solutions; Optimality .117
Exercises.123
4.5 Notes.124
5 The Simplex Method 125
5.1 Introduction.125
5.2 The Simplex Method .126
5.2.1 General Formulas.129
5.2.2 Unbounded Problems.134
5.2.3 Notation for the Simplex Method (Tableaus).135
5.2.4 Deficiencies of the Tableau.139
Contents vü
Exercises.141
5.3 The Simplex Method (Details) .144
5.3.1 Multiple Solutions.144
5.3.2 Feasible Directions and Edge Directions.145
Exercises.148
5.4 Getting Started—Artificial Variables.149
5.4.1 The Two-Phase Method. 150
5.4.2 The Big-M Method . 156
Exercises. 159
5.5 Degeneracy and Termination . 162
5.5.1 Resolving Degeneracy Using Perturbation. 167
Exercises.170
5.6 Notes.171
6 Duality and Sensitivity 173
6.1 The Dual Problem.173
Exercises.177
6.2 Duality Theory.179
6.2.1 Complementary Slackness.182
6.2.2 Interpretation of the Dual.184
Exercises.185
6.3 The Dual Simplex Method.189
Exercises.194
6.4 Sensitivity.195
Exercises.201
6.5 Parametric Linear Programming.204
Exercises.210
6.6 Notes.211
7 Enhancements of the Simplex Method 213
7.1 Introduction.213
7.2 Problems with Upper Bounds.214
Exercises.221
7.3 Column Generation.222
Exercises.227
7.4 The Decomposition Principle.227
Exercises.238
7.5 Representation of the Basis.240
7.5.1 The Product Form of the Inverse .240
7.5.2 Representation of the Basis—The LU Factorization .248
Exercises.256
7.6 Numerical Stability and Computational Efficiency.259
7.6.1 Pricing.260
7.6.2 The Initial Basis.264
7.6.3 Tolerances; Degeneracy.265
7.6.4 Scaling.266
viii Contents
7.6.5 Preprocessing.267
7.6.6 Model Formats.268
Exercises.269
7.7 Notes.270
8 Network Problems 271
8.1 Introduction.271
8.2 Basic Concepts and Examples.271
Exercises.280
8.3 Representation of the Basis.280
Exercises.287
8.4 The Network Simplex Method .287
Exercises.294
8.5 Resolving Degeneracy.295
Exercises.299
8.6 Notes.299
9 Computational Complexity of Linear Programming 301
9.1 Introduction.301
9.2 Computational Complexity.302
Exercises.304
9.3 Worst-Case Behavior of the Simplex Method.305
Exercises.308
9.4 The Ellipsoid Method.308
Exercises.313
9.5 The Average-Case Behavior of the Simplex Method.314
9.6 Notes.316
10 Interior-Point Methods for Linear Programming 319
10.1 Introduction.319
10.2 The Primal-Dual Interior-Point Method.321
10.2.1 Computational Aspects of Interior-Point Methods . . . .328
10.2.2 The Predictor-Corrector Algorithm.329
Exercises.330
10.3 Feasibility and Self-Dual Formulations.331
Exercises.334
10.4 Some Concepts from Nonlinear Optimization .334
10.5 Affine-Scaling Methods.336
Exercises.343
10.6 Path-Following Methods .344
Exercises.352
10.7 Notes.353
Contents ¡x
III Unconstrained Optimization 355
11 Basics of Unconstrained Optimization 357
11.1 Introduction.357
11.2 Optimality Conditions.357
Exercises.361
11.3 Newton's Method for Minimization.364
Exercises.369
11.4 Guaranteeing Descent.371
Exercises.374
11.5 Guaranteeing Convergence: Line Search Methods.375
11.5.1 Other Line Searches.381
Exercises.385
11.6 Guaranteeing Convergence: Trust-Region Methods.391
Exercises.398
11.7 Notes.399
12 Methods for Unconstrained Optimization 401
12.1 Introduction.401
12.2 Steepest-Descent Method.402
Exercises.408
12.3 Quasi-Newton Methods.411
Exercises.420
12.4 Automating Derivative Calculations.422
12.4.1 Finite-Difference Derivative Estimates.422
12.4.2 Automatic Differentiation.426
Exercises.429
12.5 Methods That Do Not Require Derivatives.431
12.5.1 Simulation-Based Optimization.432
12.5.2 Compass Search: A Derivative-Free Method.434
12.5.3 Convergence of Compass Search.437
Exercises.440
12.6 Termination Rules.441
Exercises.445
12.7 Historical Background.446
12.8 Notes.448
13 Low-Storage Methods for Unconstrained Problems 451
13.1 Introduction.451
13.2 The Conjugate-Gradient Method for Solving Linear Equations . . . .452
Exercises.459
13.3 Truncated-Newton Methods.460
Exercises.465
13.4 Nonlinear Conjugate-Gradient Methods.466
Exercises.469
13.5 Limited-Memory Quasi-Newton Methods .470
Contents
Exercises.473
13.6 Preconditioning.474
Exercises.477
13.7 Notes.478
IV Nonlinear Optimization 481
14 Optimality Conditions for Constrained Problems 483
14.1 Introduction.483
14.2 Optimality Conditions for Linear Equality Constraints.484
Exercises.489
14.3 The Lagrange Multipliers and the Lagrangian Function .491
Exercises.493
14.4 Optimality Conditions for Linear Inequality Constraints.494
Exercises.501
14.5 Optimality Conditions for Nonlinear Constraints.502
14.5.1 Statement of Optimality Conditions.503
Exercises.508
14.6 Preview of Methods.510
Exercises.514
14.7 Derivation of Optimality Conditions for Nonlinear Constraints . . . .515
Exercises.520
14.8 Duality.522
14.8.1 Games and Min-Max Duality.523
14.8.2 Lagrangian Duality .526
14.8.3 Wolfe Duality.532
14.8.4 More on the Dual Function.534
14.8.5 Duality in Support Vector Machines.538
Exercises.542
14.9 Historical Background.543
14.10 Notes.546
15 Feasible-Point Methods 549
15.1 Introduction.549
15.2 Linear Equality Constraints.549
Exercises.555
15.3 Computing the Lagrange Multipliers.556
Exercises.561
15.4 Linear Inequality Constraints.563
15.4.1 Linear Programming.570
Exercises.572
15.5 Sequential Quadratic Programming.573
Exercises.580
15.6 Reduced-Gradient Methods.581
Exercises.588
Contents x¡
15.7 Filter Methods.588
Exercises.597
15.8 Notes.598
16 Penalty and Barrier Methods 601
16.1 Introduction.601
16.2 Classical Penalty and Barrier Methods.602
16.2.1 Barrier Methods.603
16.2.2 Penalty Methods.610
16.2.3 Convergence.613
Exercises.617
16.3 Ill-Conditioning.618
16.4 Stabilized Penalty and Barrier Methods.619
Exercises.623
16.5 Exact Penalty Methods .623
Exercises.626
16.6 Multiplier-Based Methods.626
16.6.1 Dual Interpretation.635
Exercises.638
16.7 Nonlinear Primal-Dual Methods.640
16.7.1 Primal-Dual Interior-Point Methods.641
16.7.2 Convergence of the Primal-Dual Interior-Point Method .645
Exercises.647
16.8 Semidefinite Programming .649
Exercises.654
16.9 Notes.656
V Appendices 659
A Topics from Linear Algebra 661
A.I Introduction.661
A.2 Eigenvalues.661
A.3 Vector and Matrix Norms.662
A.4 Systems of Linear Equations .664
A.5 Solving Systems of Linear Equations by Elimination.666
A.6 Gaussian Elimination as a Matrix Factorization.669
A.6.1 Sparse Matrix Storage.675
A.7 Other Matrix Factorizations.676
A.7.1 Positive-Definite Matrices.677
A.7.2 The LDLT and Cholesky Factorizations.678
A.7.3 An Orthogonal Matrix Factorization.681
A.8 Sensitivity (Conditioning).683
A.9 The Sherman-Morrison Formula.686
A.10 Notes.688
xü Contents
B Other Fundamentals 691
B.I Introduction.691
B.2 Computer Arithmetic .691
B.3 Big-0 Notation, O(-) .693
B.4 The Gradient, Hessian, and Jacobian.694
B.5 Gradient and Hessian of a Quadratic Function.696
B.6 Derivatives of a Product.697
B.7 The Chain Rule.698
B.8 Continuous Functions; Closed and Bounded Sets.699
B.9 The Implicit Function Theorem.700
C Software 703
C.I Software.703
Bibliography 707
Index 727 |
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| author | Griva, Igor Nash, Stephen G. Sofer, Ariela |
| author_GND | (DE-588)137672012 (DE-588)128553634 (DE-588)138320195 |
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| callnumber-sort | T 257.74 |
| callnumber-subject | T - General Technology |
| classification_rvk | SK 870 |
| ctrlnum | (OCoLC)236082842 (DE-599)BVBBV035117911 |
| dewey-full | 519.7/2 519.72 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.7/2 519.72 |
| dewey-search | 519.7/2 519.72 |
| 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.BV035117911 |
| illustrated | Illustrated |
| index_date | 2024-07-02T22:20:17Z |
| indexdate | 2024-07-09T21:22:43Z |
| institution | BVB |
| isbn | 9780898716610 |
| language | English |
| lccn | 2008032477 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016785628 |
| oclc_num | 236082842 |
| open_access_boolean | |
| owner | DE-20 DE-29T DE-355 DE-BY-UBR DE-703 DE-634 DE-384 DE-188 DE-824 DE-11 |
| owner_facet | DE-20 DE-29T DE-355 DE-BY-UBR DE-703 DE-634 DE-384 DE-188 DE-824 DE-11 |
| physical | XXII, 742 S. Ill., graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | SIAM |
| record_format | marc |
| spelling | Griva, Igor Verfasser (DE-588)137672012 aut Linear and nonlinear optimization Igor Griva ; Stephen G. Nash ; Ariela Sofer 2. ed. Philadelphia SIAM 2009 XXII, 742 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Linear programming Nonlinear programming Nichtlineare Optimierung (DE-588)4128192-5 gnd rswk-swf Lineare Optimierung (DE-588)4035816-1 gnd rswk-swf Lineare Optimierung (DE-588)4035816-1 s Nichtlineare Optimierung (DE-588)4128192-5 s DE-604 Nash, Stephen G. Verfasser (DE-588)128553634 aut Sofer, Ariela Verfasser (DE-588)138320195 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016785628&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Griva, Igor Nash, Stephen G. Sofer, Ariela Linear and nonlinear optimization Linear programming Nonlinear programming Nichtlineare Optimierung (DE-588)4128192-5 gnd Lineare Optimierung (DE-588)4035816-1 gnd |
| subject_GND | (DE-588)4128192-5 (DE-588)4035816-1 |
| title | Linear and nonlinear optimization |
| title_auth | Linear and nonlinear optimization |
| title_exact_search | Linear and nonlinear optimization |
| title_exact_search_txtP | Linear and nonlinear optimization |
| title_full | Linear and nonlinear optimization Igor Griva ; Stephen G. Nash ; Ariela Sofer |
| title_fullStr | Linear and nonlinear optimization Igor Griva ; Stephen G. Nash ; Ariela Sofer |
| title_full_unstemmed | Linear and nonlinear optimization Igor Griva ; Stephen G. Nash ; Ariela Sofer |
| title_short | Linear and nonlinear optimization |
| title_sort | linear and nonlinear optimization |
| topic | Linear programming Nonlinear programming Nichtlineare Optimierung (DE-588)4128192-5 gnd Lineare Optimierung (DE-588)4035816-1 gnd |
| topic_facet | Linear programming Nonlinear programming Nichtlineare Optimierung Lineare Optimierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016785628&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT grivaigor linearandnonlinearoptimization AT nashstepheng linearandnonlinearoptimization AT soferariela linearandnonlinearoptimization |