The study of nonlinear optimization is both fundamental and a key course for applied mathematics, operations research, management science, industrial engineering, and economics at most colleges and universities.
The study of nonlinear optimization is both fundamental and a key course for applied mathematics, operations research, management science, industrial engineering, and economics at most colleges and universities.
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.
Inhaltsangabe
Chapter 1. Nonlinear Optimization Overview 1.1 Introduction 1.2 Modeling 1.3 Exercises Chapter 2. Review of Single Variable Calculus Topics 2.1 Limits 2.2 Continuity 2.3 Differentiation 2.4 Convexity Chapter 3. Single Variable Optimization 3.1 Introduction 3.2 Optimization Applications 3.3 Optimization Models Constrained Optimization by Calculus Chapter 4. Single Variable Search Methods 4.1 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 Search Chapter 5. Review of MV Calculus Topics 5.1 Introduction, Basic Theory, and Partial Derivatives 5.2 Directional Derivatives and The Gradient Chapter 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 Variables Chapter 7. Multi-variable Search Methods 7.1 Introduction 7.2 Gradient Search 7.3 Modified Newton's Method Chapter 8. Equality Constrained Optimization: Lagrange Multipliers 8.1 Introduction and Theory 8.2 Graphical Interpretation 8.3 Computational Methods 8.4 Modeling and Applications Chapter 9. Inequality Constrained Optimization; Kuhn-Tucker Methods 9.1 Introduction 9.2 Basic Theory 9.3 Graphical Interpretation and Computational Methods 9.4 Modeling and Applications Chapter 10. Method of Feasible Directions and Other Special NL Methods 10.1 Methods of Feasible Directions Numerical methods (Directional Searches) Starting Point Methods 10.2 Separable Programming 10.3 Quadratic Programming Chapter 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
