Nonlinear Optimization

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