Introduction to Applied Optimization

by Diwekar, Urmila

• ISBN13: 9780387766348
• ISBN10: 0387766340
• eBook ISBN(s): 9780387766355
• Edition: 2nd
• Format: Hardcover
• Copyright: 2008-11-01
• Publisher: Springer Nature

Summary

"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." "Introduction to Applied Optimization is intended for advanced undergraduate and graduate students and will benefit scientists from diverse areas, including engineers."--BOOK JACKET.

Table of Contents

Foreword	p. xi
Preface to the Second Edition	p. xv
Acknowledgments	p. xvii
List of Figures	p. xix
List of Tables	p. xxiii
Introduction	p. 1
Problem Formulation: A Cautionary Note	p. 3
Degrees of Freedom Analysis	p. 3
Objective Function, Constraints, and Feasible Region	p. 4
Numerical Optimization	p. 5
Types of Optimization Problems	p. 7
Summary	p. 7
Bibliography	p. 8
Exercises	p. 9
Linear Programming	p. 11
The Simplex Method	p. 12
Infeasible Solution	p. 17
Unbounded Solution	p. 19
Multiple Solutions	p. 21
Sensitivity Analysis	p. 23
Other Methods	p. 26
Hazardous Waste Blending Problem as an LP	p. 28
Summary	p. 34
Bibliography	p. 34
Exercises	p. 35
Nonlinear Programming	p. 41
Convex and Concave Functions	p. 44
Unconstrained NLP	p. 47
Necessary and Sufficient Conditions and Constrained NLP	p. 52
Constraint Qualification	p. 62
Sensitivity Analysis	p. 62
Numerical Methods	p. 64
Global Optimization and Interval Newton Method	p. 68
Hazardous Waste Blending: An NLP	p. 69
Summary	p. 71
Bibliography	p. 72
Exercises	p. 72
Discrete Optimization	p. 77
Tree and Network Representation	p. 78
Branch-and-Bound for IP	p. 80
Numerical Methods for IP, MILP, and MINLP	p. 84
Probabilistic Methods	p. 99
Hazardous Waste Blending: A Combinatorial Problem	p. 107
The OA-based MINLP Approach	p. 109
The Two-Stage Approach with SA-NLP	p. 109
A Branch-and-Bound Procedure	p. 112
Summary	p. 116
Bibliography	p. 116
Exercises	p. 118
Optimization Under Uncertainty	p. 125
Types of Problems and Generalized Representation	p. 131
Chance Constrained Programming Method	p. 139
L-shaped Decomposition Method	p. 142
Uncertainty Analysis and Sampling	p. 146
Specifying Uncertainty Using Probability Distributions	p. 147
Sampling Techniques in Stochastic Modeling	p. 148
Sampling Accuracy and the Decomposition Methods	p. 156
Implications of Sample Size in Stochastic Modeling	p. 156
Stochastic Annealing	p. 157
Hazardous Waste Blending Under Uncertainty	p. 164
The Stochastic Optimization Problem	p. 168
Results and Discussion	p. 170
Summary	p. 172
Bibliography	p. 172
Exercises	p. 175
Multiobjective Optimization	p. 179
Nondominated Set	p. 183
Solution Methods	p. 186
Weighting Method	p. 189
Constraint Method	p. 194
Goal Programming Method	p. 197
Hazardous Waste Blending and Value of Research	p. 199
Variance as an Attribute: The Analysis of Uncertainty	p. 200
Base Objective: Minimization of Frit Mass	p. 200
Robustness: Minimizing Variance	p. 201
Reducing Uncertainty: Minimizing the Time Devoted to Research	p. 203
Discussion: The Implications of Uncertainty	p. 204
Summary	p. 208
Bibliography	p. 208
Exercises	p. 212
Optimal Control And Dynamic Optimization	p. 215
Calculus of Variations	p. 219
Maximum Principle	p. 224
Dynamic Programming	p. 227
Stochastic Processes and Dynamic Programming	p. 231
Ito's Lemma	p. 235
Dynamic Programming Optimality Conditions	p. 236
Reversal of Blending: Optimizing a Separation Process	p. 240
Calculus of Variations Formulation	p. 247
Maximum Principle Formulation	p. 248
Method of Steepest Ascent of Hamiltonian	p. 250
Combining Maximum Principle and NLP Techniques	p. 251
Uncertainties in Batch Distillation	p. 253
Relative Volatility: An Ito Process	p. 254
Optimal Reflux Profile: Deterministic Case	p. 257
Case in Which Uncertainties Are Present	p. 258
State Variable and Relative Volatility: The Two Ito Processes	p. 260
Coupled Maximum Principle and NLP Approach for the Uncertain Case	p. 262
Summary	p. 265
Bibliography	p. 265
Exercises	p. 266
Appendix	p. 279
Index	p. 283
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