Nonlinear optimization: models and applications

Table 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

Nonlinear Optimization: Models and Applications presents the concepts in several ways to foster understanding. Geometric interpretation: is used to re-enforce the concepts and to foster understanding of the mathematical procedures. The student sees that many problems can be analyzed, and approximate solutions found before analytical solutions techniques are applied. Numerical approximations: early on, the student is exposed to numerical techniques. These numerical procedures are algorithmic and iterative. Worksheets are provided in Excel, MATLAB®, and Maple™ to facilitate the procedure. Algorithms: all algorithms are provided with a step-by-step format. Examples follow the summary to illustrate its use and application.

Nonlinear Optimization: Models and Applications:

Emphasizes process and interpretation throughout
Presents a general classification of optimization problems
Addresses situations that lead to models illustrating many types of optimization problems
Emphasizes model formulations
Addresses a special class of problems that can be solved using only elementary calculus
Emphasizes model solution and model sensitivity analysis