Part I: Mathematical Review.
1. Methods of Proof and Some Notation.
2. Vector Spaces and Matrices.
4. Concepts from geometry.
5. Elements of Calculus.
Part II: Unconstrained Optimization.
6. Basics of Set-Constrained and Unconstrained Optimization.
7. One-Dimensional Search Methods.
8. Gradient Methods.
9. Newton's Method.
10. Conjugate Direction Methods.
11. Quasi-Newton Methods.
12. Solving Linear Equations.
13. Unconstrained Optimization and Neural Networks.
14. Global Search Algorithms.
Part III: Linear Programming.
15. Introduction to Linear Programming.
16. Simplex Method.
18. Nonsimplex Methods.
Part IV: Nonlinear Constrained Optimization
19. Problems with Equality Constraints.
20. Problems with Inequality Constraints.
21. Convex Optimization Problems.
22. Algorithms for Constrained Optimization.
23. Multiobjective Optimization.
- Major topics, including the Nelder-Mead algorithm and the simulated annealing algorithm, have been added to the new edition.
- A new chapter on multi-objective optimization discusses problems with multiple-objective functions and how they are treated; Pareto solutions; and algorithms for multi-objective problems, i.e., genetic algorithms.
- Additional, class-tested exercises are included in almost every chapter and some examples use MATLAB.
- The bibliography includes new references.
- The Instructor's Manual has been updated to include fully worked-out solutions to each of the new exercises.
- This book provides an up-to-date, accessible introduction to optimization theory and methods with an emphasis on engineering design
- A review of the required mathematical background is provided.
- The book reviews basic definitions, notations and relations from linear algebra, geometry and calculus, followed by unconstrained optimization problems.
- Existing topics were modified to include improve to the organization of the book and to promote classroom discussion.