Introduction to Applied Optimization

Foreword
Preface: Second Edition
Preface: Third Edition
Acknowledgments for the First Edition
Contents
List of Figures
List of Tables
Author Biography
1 Introduction
	1.1 Problem Formulation: A Cautionary Note
	1.2 Degrees of Freedom Analysis
	1.3 Objective Function, Constraints, and Feasible Region
	1.4 Numerical Optimization
	1.5 Types of Optimization Problems
	1.6 Summary
	Bibliography
2 Linear Programming
	2.1 The Simplex Method
	2.2 Infeasible Solution
	2.3 Unbounded Solution
	2.4 Multiple Solutions
	2.5 Degeneracy in LP
	2.6 Sensitivity Analysis
	2.7 Other Methods
	2.8 Hazardous Waste Blending Problem as an LP
	2.9 Sustainable Mercury Management: An LP
		2.9.1 Mercury Management Approach
		2.9.2 Watershed Based Trading
		2.9.3 Trading Optimization Model Formulation
		2.9.4 Savannah River Watershed Details
			Technology Details
			Trading Details
		2.9.5  LP Problem Details
			Industry Details
			Technology Details
			Results and Discussions
	2.10 Summary
	Bibliography
3 Nonlinear Programming
	3.1 Convex and Concave Functions
	3.2 Unconstrained NLP
	3.3 Necessary and Sufficient Conditions and Constrained NLP
	3.4 Constraint Qualification
	3.5 Sensitivity Analysis
	3.6 Numerical Methods
	3.7 Global Optimization and Interval Newton Method
	3.8 What to Do When NLP Algorithm is Not Converging
	3.9 Hazardous Waste Blending: An NLP
	3.10 Sustainable Mercury Management: An NLP
	3.11 Summary
	Bibliography
4 Discrete Optimization
	4.1 Tree and Network Representation
	4.2 Branch-and-Bound for IP
	4.3 Numerical Methods for IP, MILP, and MINLP
	4.4 Probabilistic Methods
	4.5 Hazardous Waste Blending: A Combinatorial Problem
		4.5.1 The OA-based MINLP Approach
		4.5.2 The Two-Stage Approach with SA-NLP
		4.5.3 A Branch-and-Bound Procedure
	4.6 Sustainable Mercury Management: A Combinatorial Problem
	4.7 Summary
	Bibliography
5 Optimization Under Uncertainty
	5.1 Types of Problems and Generalized Representation
	5.2 Chance Constrained Programming Method
	5.3 L-shaped Decomposition Method
	5.4 Uncertainty Analysis and Sampling
		5.4.1 Specifying Uncertainty Using Probability Distributions
		5.4.2 Sampling Techniques in Stochastic Modeling
		5.4.3 Sampling Accuracy and the Decomposition Methods
		5.4.4 Implications of Sample Size in Stochastic Modeling
	5.5  Stochastic Annealing
	5.6 Hazardous Waste Blending Under Uncertainty
		Characterization of Uncertainties in the Model
		5.6.1 The Stochastic Optimization Problem
		5.6.2 Results and Discussion
	5.7 Sustainable Mercury Management: A Stochastic Optimization Problem
		5.7.1 The Chance Constrained Programming Formulation
			Results and Discussions
		5.7.2 A Two-stage Stochastic Programming Formulation
			Results and Discussions
	5.8 Summary
	Bibliography
6 Multiobjective Optimization
	6.1 Nondominated Set
	6.2 Solution Methods
		6.2.1 Weighting Method
		6.2.2 Constraint Method
		6.2.3 Goal Programming Method
	6.3 Hazardous Waste Blending and Value of Research
		6.3.1 Variance as an Attribute: The Analysis of Uncertainty
		6.3.2 Base Objective: Minimization of Frit Mass
		6.3.3 Robustness: Minimizing Variance
		6.3.4 Reducing Uncertainty: Minimizing the Time Devoted to Research
		6.3.5 Discussion: The Implications of Uncertainty
	6.4 Sustainable Mercury Management: A Multiobjective Optimization Problem
		6.4.1 Health Care Cost
		6.4.2 The Multiobjective Optimization Formulation
	6.5 Summary
	Bibliography
7 Optimal Control and Dynamic Optimization
	7.1 Calculus of Variations
	7.2 Maximum Principle
	7.3 Dynamic Programming
	7.4 Stochastic Processes and Stochastic Optimal Control
		7.4.1 Ito's Lemma
		7.4.2 Dynamic Programming Optimality Conditions
		7.4.3 Stochastic Maximum Principle
	7.5 Reversal of Blending: Optimizing a Separation Process
		7.5.1 Calculus of Variations Formulation
		7.5.2 Maximum Principle Formulation
		7.5.3 Method of Steepest Ascent of Hamiltonian
		7.5.4 Combining Maximum Principle and NLP Techniques
		7.5.5 Uncertainties in Batch Distillation
		7.5.6 Relative Volatility: An Ito Process
		7.5.7 Optimal Reflux Profile: Deterministic Case
		7.5.8 Case in Which Uncertainties Are Present
		7.5.9 State Variable and Relative Volatility: The Two Ito Processes
		7.5.10 Coupled Maximum Principle and NLP Approach for the Uncertain Case
	7.6 Sustainable Mercury Management: An Optimal Control Problem
		7.6.1 Mercury Bioaccumulation
		7.6.2 Mercury pH Control Model
		7.6.3 Deterministic Optimal Control
			Optimality Condition
			Adjoint Equations
		7.6.4 Stochastic Optimal Control
			Optimality Condition
			Adjoint Equations
		7.6.5 Results and Discussions
			Lake A
	7.7 Summary
	Bibliography
Appendix A
Appendix B
Index