Nonlinear Optimization

Dr. William P. Fox is a professor in the Department of Defense Analysis at the Naval Postgraduate School and currently teaches a three course sequence in mathematical modeling for decision making. He received his Ph.D. at Clemson University. He has taught at the United States Military Academy and at Francis Marion University where he was the chair of mathematics for eight years. He has many publications and scholarly activities including sixteen books, one hundred and fifty journal articles, and about one hundred and fifty conference presentations, and workshops. He was Past- President of the Military Application Society of INFORMS and is the current Vice Chair for Programs for BIG SIGMAA.

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• Chapter 1. Nonlinear Optimization Overview1.1 Introduction 1.2 Modeling 1.3 ExercisesChapter 2. Review of Single Variable Calculus Topics 2.1 Limits 2.2 Continuity 2.3 Differentiation 2.4 ConvexityChapter 3. Single Variable Optimization3.1 Introduction 3.2 Optimization Applications 3.3 Optimization Models Constrained Optimization by CalculusChapter 4. Single Variable Search Methods4.1 Introduction 4.2 Unrestricted Search 4.3 Dichotomous Search 4.4 Golden Section Search 4.5 Fibonacci Search 4.6 Newton’s Method 4.7 Bisection Derivative SearchChapter 5. Review of MV Calculus Topics 5.1 Introduction, Basic Theory, and Partial Derivatives 5.2 Directional Derivatives and The GradientChapter 6. MV Optimization 6.1 Introduction 6.2 The Hessian 6.3 Unconstrained Optimization Convexity and The Hessian Matrix Max and Min Problems with Several VariablesChapter 7. Multi-variable Search Methods7.1 Introduction 7.2 Gradient Search 7.3 Modified Newton’s MethodChapter 8. Equality Constrained Optimization: Lagrange Multipliers8.1 Introduction and Theory 8.2 Graphical Interpretation 8.3 Computational Methods 8.4 Modeling and ApplicationsChapter 9. Inequality Constrained Optimization; Kuhn-Tucker Methods9.1 Introduction 9.2 Basic Theory 9.3 Graphical Interpretation and Computational Methods 9.4 Modeling and ApplicationsChapter 10. Method of Feasible Directions and Other Special NL Methods10.1 Methods of Feasible Directions Numerical methods (Directional Searches) Starting Point Methods 10.2 Separable Programming 10.3 Quadratic ProgrammingChapter 11. Dynamic Programming 11.1 Introduction 11.2 Continuous Dynamic Programming 11.3 Modeling and Applications with Continuous DP 11.4 Discrete Dynamic Programming 11.5 Modeling and Applications with Discrete Dynamic Programming