Introduction to Applied Optimization / Edition 2

Introduction to Applied Optimization / Edition 2

by Urmila Diwekar
     
 

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ISBN-10: 0387766340

ISBN-13: 9780387766348

Pub. Date: 08/28/2008

Publisher: Springer US

This text presents a multi-disciplined view of optimization, providing students and researchers with a thorough examination of algorithms, methods, and tools from diverse areas of optimization without introducing excessive theoretical detail. This second edition includes additional topics, including global optimization and a real-world case study using important

Overview

This text presents a multi-disciplined view of optimization, providing students and researchers with a thorough examination of algorithms, methods, and tools from diverse areas of optimization without introducing excessive theoretical detail. This second edition includes additional topics, including global optimization and a real-world case study using important concepts from each chapter.

Product Details

ISBN-13:
9780387766348
Publisher:
Springer US
Publication date:
08/28/2008
Series:
Springer Optimization and Its Applications Series , #22
Edition description:
2nd ed. 2008
Pages:
291
Product dimensions:
6.10(w) x 9.30(h) x 0.80(d)

Table of Contents

Foreword xi

Preface to the Second Edition xv

Acknowledgments xvii

List of Figures xix

List of Tables xxiii

1 Introduction 1

1.1 Problem Formulation: A Cautionary Note 3

1.2 Degrees of Freedom Analysis 3

1.3 Objective Function, Constraints, and Feasible Region 4

1.4 Numerical Optimization 5

1.5 Types of Optimization Problems 7

1.6 Summary 7

Bibliography 8

Exercises 9

2 Linear Programming 11

2.1 The Simplex Method 12

2.2 Infeasible Solution 17

2.3 Unbounded Solution 19

2.4 Multiple Solutions 21

2.5 Sensitivity Analysis 23

2.6 Other Methods 26

2.7 Hazardous Waste Blending Problem as an LP 28

2.8 Summary 34

Bibliography 34

Exercises 35

3 Nonlinear Programming 41

3.1 Convex and Concave Functions 44

3.2 Unconstrained NLP 47

3.3 Necessary and Sufficient Conditions and Constrained NLP 52

3.4 Constraint Qualification 62

3.5 Sensitivity Analysis 62

3.6 Numerical Methods 64

3.7 Global Optimization and Interval Newton Method 68

3.8 Hazardous Waste Blending: An NLP 69

3.9 Summary 71

Bibliography 72

Exercises 72

4 Discrete Optimization 77

4.1 Tree and Network Representation 78

4.2 Branch-and-Bound for IP 80

4.3 Numerical Methods for IP, MILP, and MINLP 84

4.4 Probabilistic Methods 99

4.5 Hazardous Waste Blending: A Combinatorial Problem 107

4.5.1 The OA-based MINLP Approach 109

4.5.2 The Two-Stage Approach with SA-NLP 109

4.5.3 A Branch-and-Bound Procedure 112

4.6 Summary 116

Bibliography 116

Exercises 118

5 Optimization Under Uncertainty 125

5.1 Types of Problems and Generalized Representation 131

5.2 Chance Constrained Programming Method 139

5.3 L-shaped Decomposition Method 142

5.4Uncertainty Analysis and Sampling 146

5.4.1 Specifying Uncertainty Using Probability Distributions 147

5.4.2 Sampling Techniques in Stochastic Modeling 148

5.4.3 Sampling Accuracy and the Decomposition Methods 156

5.4.4 Implications of Sample Size in Stochastic Modeling 156

5.5 Stochastic Annealing 157

5.6 Hazardous Waste Blending Under Uncertainty 164

5.6.1 The Stochastic Optimization Problem 168

5.6.2 Results and Discussion 170

5.7 Summary 172

Bibliography 172

Exercises 175

6 Multiobjective Optimization 179

6.1 Nondominated Set 183

6.2 Solution Methods 186

6.2.1 Weighting Method 189

6.2.2 Constraint Method 194

6.2.3 Goal Programming Method 197

6.3 Hazardous Waste Blending and Value of Research 199

6.3.1 Variance as an Attribute: The Analysis of Uncertainty 200

6.3.2 Base Objective: Minimization of Frit Mass 200

6.3.3 Robustness: Minimizing Variance 201

6.3.4 Reducing Uncertainty: Minimizing the Time Devoted to Research 203

6.3.5 Discussion: The Implications of Uncertainty 204

6.4 Summary 208

Bibliography 208

Exercises 212

7 Optimal Control And Dynamic Optimization 215

7.1 Calculus of Variations 219

7.2 Maximum Principle 224

7.3 Dynamic Programming 227

7.4 Stochastic Processes and Dynamic Programming 231

7.4.1 Ito's Lemma 235

7.4.2 Dynamic Programming Optimality Conditions 236

7.5 Reversal of Blending: Optimizing a Separation Process 240

7.5.1 Calculus of Variations Formulation 247

7.5.2 Maximum Principle Formulation 248

7.5.3 Method of Steepest Ascent of Hamiltonian 250

7.5.4 Combining Maximum Principle and NLP Techniques 251

7.5.5 Uncertainties in Batch Distillation 253

7.5.6 Relative Volatility: An Ito Process 254

7.5.7 Optimal Reflux Profile: Deterministic Case 257

7.5.8 Case in Which Uncertainties Are Present 258

7.5.9 State Variable and Relative Volatility: The Two Ito Processes 260

7.5.10 Coupled Maximum Principle and NLP Approach for the Uncertain Case 262

7.6 Summary 265

Bibliography 265

Exercises 266

Appendix 279

Index 283

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