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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.
List of contents
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
About the author
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.
Summary
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.
