Nonlinear programming: theory and algorithms
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Wiley
1993
|
| Edition: | 2. ed. |
| Series: | Wiley-interscience series in discrete mathematics and optimization
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 638 S. graph. Darst. |
| ISBN: | 0471557935 |
Staff View
MARC
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| 245 | 1 | 0 | |a Nonlinear programming |b theory and algorithms |c Mokhtar S. Bazaraa ; Hanif D. Sherali ; C. M. Shetty |
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Record in the Search Index
| _version_ | 1804122407429996544 |
|---|---|
| adam_text | Contents
Chapter 1 Introduction 1
1.1 Problem Statement and Basic Definitions 2
1.2 Some Illustrative Examples 4
1.3 Some Guidelines for Model Construction 21
Exercises 24
Notes and References 27
Part 1 Convex Analysis 31
Chapter 2 Convex Sets 33
2.1 Convex Hulls 34
2.2 Closure and Interior of a Set 38
2.3 Weierstrass Theorem 41
2.4 Separation and Support of Sets 42
2.5 Convex Cones and Polarity 52
2.6 Polyhedral Sets, Extreme Points, and Extreme
Directions 54
2.7 Linear Programming and the Simplex Method 62
Exercises 71
Notes and References 76
Chapter 3 Convex Functions and Generalizations 78
3.1 Definitions and Basic Properties 79
3.2 Subgradients of Convex Functions 83
3.3 Differentiable Convex Functions 88
3.4 Minima and Maxima of Convex Functions 99
3.5 Generalizations of Convex Functions 107
Exercises 117
Notes and References 125
xi
xii Contents
Part 2 Optimality Conditions and Duality 129
Chapter 4 The Fritz John and the Karush Kuhn Tucker Optimality
Conditions 131
4.1 Unconstrained Problems 132
4.2 Problems with Inequality Constraints 138
4.3 Problems with Inequality and Equality
Constraints 156
4.4 Second Order Necessary and Sufficient Optimality
Conditions for Constrained Problems 167
Exercises 173
Notes and References 182
Chapter 5 Constraint Qualifications 184
5.1 The Cone of Tangents 184
5.2 Other Constraint Qualifications 188
5.3 Problems with Inequality and Equality
Constraints 191
Exercises 195
Notes and References 198
Chapter 6 Lagrangian Duality and Saddle Point Optimality Conditions 199
6.1 The Lagrangian Dual Problem 200
6.2 Duality Theorems and Saddle Point Optimality
Conditions 203
6.3 Properties of the Dual Function 214
6.4 Formulating and Solving the Dual Problem 222
6.5 Getting the Primal Solution 228
6.6 Linear and Quadratic Programs 231
Exercises 233
Notes and References 241
Part 3 Algorithms and Their Convergence 243
Chapter 7 The Concept of an Algorithm 244
7.1 Algorithms and Algorithmic Maps 244
7.2 Closed Maps and Convergence 247
7.3 Composition of Mappings 251
7.4 Comparison Among Algorithms 255
Exercises 258
Notes and References 263
Chapter 8 Unconstrained Optimization 265
8.1 Line Search Without Using Derivatives 266
8.2 Line Search Using Derivatives 276
8.3 Some Practical Line Search Methods 279
8.4 Closedness of the Line Search Algorithmic Map 282
8.5 Multidimensional Search Without Using
Derivatives 283
Contents xili
8.6 Multidimensional Search Using Derivatives 300
8.7 Modification of Newton s Method: Levenberg
Marquardt and Trust Region Methods 312
8.8 Methods Using Conjugate Directions: Quasi Newton
and Conjugate Gradient Methods 315
8.9 Subgradient Optimization Methods 339
Exercises 344
Notes and References 355
Chapter 9 Penalty and Barrier Functions 360
9.1 The Concept of Penalty Functions 361
9.2 Exterior Penalty Function Methods 365
9.3 Exact Absolute Value and Augmented Lagrangian
Penalty Methods 372
9.4 Barrier Function Methods 385
9.5 A Polynomial Time Algorithm for Linear
Programming Based on a Barrier Function 392
Exercises 399
Notes and References 406
Chapter 10 Methods of Feasible Directions 408
10.1 The Method of Zoutendijk 409
10.2 Convergence Analysis of the Method of
Zoutendijk 423
10.3 Successive Linear Programming Approach 432
10.4 Successive Quadratic Programming or Projected
Lagrangian Approach 438
10.5 The Gradient Projection Method of Rosen 448
10.6 The Method of Reduced Gradient of Wolfe and the
Generalized Reduced Gradient Method 458
10.7 The Convex Simplex Method of Zangwill 466
10.8 Effective First and Second Order Variants of the
Reduced Gradient Method 471
Exercises 474
Notes and References 489
Chapter 11 Linear Complementary Problem, and Quadratic, Separable,
Fractional, and Geometric Programming 493
11.1 The Linear Complementary Problem 494
11.2 Quadratic Programming 503
11.3 Separable Programming 509
11.4 Linear Fractional Programming 524
11.5 Geometric Programming 531
Exercises 538
Notes and References 550
Appendix A Mathematical Review 554
Appendix B Summary of Convexity, Optimality
Conditions, and Duality 565
Bibliography 576
Index 627
|
| any_adam_object | 1 |
| author | Bazaraa, Mokhtar S. 1943- Sherali, Hanif D. 1952- Shetty, Chitharanjan M. 1929- |
| author_GND | (DE-588)13576856X (DE-588)135768586 (DE-588)135768608 |
| author_facet | Bazaraa, Mokhtar S. 1943- Sherali, Hanif D. 1952- Shetty, Chitharanjan M. 1929- |
| author_role | aut aut aut |
| author_sort | Bazaraa, Mokhtar S. 1943- |
| author_variant | m s b ms msb h d s hd hds c m s cm cms |
| building | Verbundindex |
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| callnumber-search | T57.8 |
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| callnumber-subject | T - General Technology |
| classification_rvk | SK 870 |
| classification_tum | MAT 916f |
| ctrlnum | (OCoLC)26543666 (DE-599)BVBBV008042813 |
| dewey-full | 519.7/6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.7/6 |
| dewey-search | 519.7/6 |
| dewey-sort | 3519.7 16 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV008042813 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:13:23Z |
| institution | BVB |
| isbn | 0471557935 |
| language | English |
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| publisher | Wiley |
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| series2 | Wiley-interscience series in discrete mathematics and optimization |
| spelling | Bazaraa, Mokhtar S. 1943- Verfasser (DE-588)13576856X aut Nonlinear programming theory and algorithms Mokhtar S. Bazaraa ; Hanif D. Sherali ; C. M. Shetty 2. ed. New York [u.a.] Wiley 1993 XIII, 638 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley-interscience series in discrete mathematics and optimization Niet-lineaire programmering gtt Nonlinear programming Nichtlineare Optimierung (DE-588)4128192-5 gnd rswk-swf Optimierung (DE-588)4043664-0 gnd rswk-swf Optimierung (DE-588)4043664-0 s Nichtlineare Optimierung (DE-588)4128192-5 s 1\p DE-604 Sherali, Hanif D. 1952- Verfasser (DE-588)135768586 aut Shetty, Chitharanjan M. 1929- Verfasser (DE-588)135768608 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005291726&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 |
| spellingShingle | Bazaraa, Mokhtar S. 1943- Sherali, Hanif D. 1952- Shetty, Chitharanjan M. 1929- Nonlinear programming theory and algorithms Niet-lineaire programmering gtt Nonlinear programming Nichtlineare Optimierung (DE-588)4128192-5 gnd Optimierung (DE-588)4043664-0 gnd |
| subject_GND | (DE-588)4128192-5 (DE-588)4043664-0 |
| title | Nonlinear programming theory and algorithms |
| title_auth | Nonlinear programming theory and algorithms |
| title_exact_search | Nonlinear programming theory and algorithms |
| title_full | Nonlinear programming theory and algorithms Mokhtar S. Bazaraa ; Hanif D. Sherali ; C. M. Shetty |
| title_fullStr | Nonlinear programming theory and algorithms Mokhtar S. Bazaraa ; Hanif D. Sherali ; C. M. Shetty |
| title_full_unstemmed | Nonlinear programming theory and algorithms Mokhtar S. Bazaraa ; Hanif D. Sherali ; C. M. Shetty |
| title_short | Nonlinear programming |
| title_sort | nonlinear programming theory and algorithms |
| title_sub | theory and algorithms |
| topic | Niet-lineaire programmering gtt Nonlinear programming Nichtlineare Optimierung (DE-588)4128192-5 gnd Optimierung (DE-588)4043664-0 gnd |
| topic_facet | Niet-lineaire programmering Nonlinear programming Nichtlineare Optimierung Optimierung |
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