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"...an excellent introduction to optimization theory..." (Journal of Mathematical Psychology, 2002)
"A textbook for a one-semester course on optimization theory and methods at the senior undergraduate or beginning graduate level." (SciTech Book News, Vol. 26, No. 2, June 2002)
Explore the latest applications of optimization theory and methods
Optimization is central to any problem involving decision making in many disciplines, such as engineering, mathematics, statistics, economics, and computer science. Now, more than ever, it is increasingly vital to have a firm grasp of the topic due to the rapid progress in computer technology, including the development and availability of user-friendly software, high-speed and parallel processors, and networks. Fully updated to reflect modern developments in the field, An Introduction to Optimization, Third Edition fills the need for an accessible, yet rigorous, introduction to optimization theory and methods.
The book begins with a review of basic definitions and notations and also provides the related fundamental background of linear algebra, geometry, and calculus. With this foundation, the authors explore the essential topics of unconstrained optimization problems, linear programming problems, and nonlinear constrained optimization. An optimization perspective on global search methods is featured and includes discussions on genetic algorithms, particle swarm optimization, and the simulated annealing algorithm. In addition, the book includes an elementary introduction to artificial neural networks, convex optimization, and multi-objective optimization, all of which are of tremendous interest to students, researchers, and practitioners.
Additional features of the Third Edition include:
Numerous diagrams and figures found throughout the text complement the written presentation of key concepts, and each chapter is followed by MATLAB exercises and drill problems that reinforce the discussed theory and algorithms. With innovative coverage and a straightforward approach, An Introduction to Optimization, Third Edition is an excellent book for courses in optimization theory and methods at the upper-undergraduate and graduate levels. It also serves as a useful, self-contained reference for researchers and professionals in a wide array of fields.
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.