Introduction to applied optimization:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Norwell, Mass.
Kluwer Acad. Publ.
2003
|
| Schriftenreihe: | Applied optimization
80 |
| Schlagworte: | |
| Online-Zugang: | Table of contents Inhaltsverzeichnis |
| Beschreibung: | XV, 335 S. Ill., graph. Darst. |
| ISBN: | 1402074565 |
Internformat
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| 245 | 1 | 0 | |a Introduction to applied optimization |c Urmila M. Diwekar |
| 264 | 1 | |a Norwell, Mass. |b Kluwer Acad. Publ. |c 2003 | |
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Datensatz im Suchindex
| _version_ | 1804130004786741248 |
|---|---|
| adam_text | CONTENTS
FOREWORD XI
AcKNOWLEDCEMENTS XV
1 INTRODUCTION 1
1.1 Problem Formulation: A Cautionary Note 3
1.2 Degrees of Freedom Analysis 4
1.3 Objective Function, Constraints, and Feasible Region .... 5
1.4 Numerical Optimization 6
1.5 Types of Optimization Problems 7
1.6 Summary 8
2 Linear Programming 13
2.1 The Simplex Method 14
2.2 lnfeasible Solution 21
2.3 Unbounded Solution 23
2.4 Multiple Solutions 25
2.5 Sensitivity Analysis 28
2.6 Other Methods 31
2.7 Hazardous Waste Blending Problem as an LP 35
2.8 Summary 43
3 Nonlinear Programming 51
3.1 Convex and Concave Functions 55
3.2 Unconstrained NLP 56
3.3 Necessary and Sufficient Conditions, and Constrained NLP 62
3.4 Sensitivity Analysis 73
3.5 Numerical Methods 75
3.6 Hazardous Waste Blending: An NLP 79
3.7 Summary 83
4 Discrete Optimization 89
4.1 Tree and Network Representation 90
4.2 Branch and Bound for IP 92
4.3 Numerical Methods for IP, MILP, and MINLP 98
4.4 Probabilistic Methods 114
4.5 Hazardous Waste Blending: A Combinatorial Problem ... 123
4.5.1 The OA based MINLP Approach 125
4.5.2 The Two stage Approach with SA NLP 126
4.5.3 A Branch and Bound Procedure 129
4.6 Summary 134
viü Introduction to Applied Optimization
5 Optimization Under Uncertainty 145
5.1 Types of Problems and Generalized Representation 151
5.2 Chance Constrained Programming Method 160
5.3 L shaped Decomposition Method 162
5.4 Uncertainty Analysis and Sampling 169
5.4.1 Specifying Uncertainty UsingProbabilityDistributionsl70
5.4.2 Sampling Techniques in Stochastic Modeling 170
5.4.3 Sampling Accuracy and the Decomposition Methods 179
5.4.4 Implications of Sample Size in Stochastic Modeling . 182
5.5 Stochastic Annealing: An Efficient Algorithm for Combina
torial Optimization under Uncertainty 182
5.6 Hazardous Waste Blending under Uncertainty 190
5.6.1 The Stochastic Optimization Problem 195
5.6.2 Results and Discussion 198
5.7 Summary 201
6 Multi objective Optimization 209
6.1 Nondominated Set 212 (
6.2 Solution Methods 218
6.2.1 Weighting Method 222
6.2.2 Constraint Method 226
6.2.3 Goal Programming Method 230
6.3 Hazardous Waste Blending and Value of Research: An MOP 232
6.3.1 Variance as an Attribute: The Analysis of Uncertainty 234
6.3.2 Base Objective: Minimization of Frit Mass 235
6.3.3 Robustness: Minimizing Variance 235
6.3.4 Reducing Uncertainty: Minimizing the Time De
voted to Research 238
6.3.5 Discussion: The Implications of Uncertainty 241
6.4 Summary 245
7 optimal control And Dynamic Optimization 255
7.1 Calculus of Variations 260
7.2 Maximum Principle 265
7.3 Dynamic Programming 268
7.4 Stochastic Dynamic Programming 273
7.4.1 Ito s Lemma 275
7.4.2 Dynamic Programming Optimality Conditions .... 277
7.5 Reversal of Blending: Optimizing a Separation Process . . . 281
7.5.1 Calculus of Variations Formulation 291
7.5.2 Maximum Principle Formulation 292
7.5.3 Method of Steepest Ascent of Hamiltonian 294
7.5.4 Combining Maximum Principle and NLP Techniques 295
7.5.5 Uncertainties in Batch Distillation 298
ix
7.5.6 Relative Volatility: An Ito Process 299
7.5.7 Optimal Reflux Profile: Deterministic Case 301
7.5.8 Case in Which Uncertainties are Present 303
7.5.9 State Variable and Relative Volatility: The Two Ito
Processes 305
7.5.10 Coupled Maximum Principle and NLP Approach for
the Uncertain Case 307
7.6 Summary 310
Appendix A 317
Appendix B 323
Index 325
|
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| dewey-full | 519.3 519.321 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.3 519.3 21 |
| dewey-search | 519.3 519.3 21 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
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| indexdate | 2024-07-09T19:14:08Z |
| institution | BVB |
| isbn | 1402074565 |
| language | English |
| lccn | 2003051643 |
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| physical | XV, 335 S. Ill., graph. Darst. |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Kluwer Acad. Publ. |
| record_format | marc |
| series | Applied optimization |
| series2 | Applied optimization |
| spelling | Diwekar, Urmila M. Verfasser (DE-588)1089790554 aut Introduction to applied optimization Urmila M. Diwekar Norwell, Mass. Kluwer Acad. Publ. 2003 XV, 335 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Applied optimization 80 Optimaliseren gtt Optimisation mathématique Mathematical optimization Anwendung (DE-588)4196864-5 gnd rswk-swf Optimierung (DE-588)4043664-0 gnd rswk-swf Optimierung (DE-588)4043664-0 s Anwendung (DE-588)4196864-5 s DE-604 Applied optimization 80 (DE-604)BV010841718 80 http://www.loc.gov/catdir/toc/fy038/2003051643.html Table of contents HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010331242&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Diwekar, Urmila M. Introduction to applied optimization Applied optimization Optimaliseren gtt Optimisation mathématique Mathematical optimization Anwendung (DE-588)4196864-5 gnd Optimierung (DE-588)4043664-0 gnd |
| subject_GND | (DE-588)4196864-5 (DE-588)4043664-0 |
| title | Introduction to applied optimization |
| title_auth | Introduction to applied optimization |
| title_exact_search | Introduction to applied optimization |
| title_full | Introduction to applied optimization Urmila M. Diwekar |
| title_fullStr | Introduction to applied optimization Urmila M. Diwekar |
| title_full_unstemmed | Introduction to applied optimization Urmila M. Diwekar |
| title_short | Introduction to applied optimization |
| title_sort | introduction to applied optimization |
| topic | Optimaliseren gtt Optimisation mathématique Mathematical optimization Anwendung (DE-588)4196864-5 gnd Optimierung (DE-588)4043664-0 gnd |
| topic_facet | Optimaliseren Optimisation mathématique Mathematical optimization Anwendung Optimierung |
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