"...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:
New discussions of semidefinite programming and Lagrangian algorithms
A new chapter on global search methods
A new chapter on multipleobjective optimization
New and modified examples and exercises in each chapter as well as an updated bibliography containing new references
An updated Instructor's Manual with fully worked-out solutions to the exercises
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.
Content:
Chapter 1 Methods of Proof and Some Notation (pages 1โ6):
Chapter 2 Vector Spaces and Matrices (pages 7โ22):
Chapter 3 Transformations (pages 23โ41):
Chapter 4 Concepts from Geometry (pages 43โ51):
Chapter 5 Elements of Calculus (pages 53โ75):
Chapter 6 Basics of Set?Constrained and Unconstrained Optimization (pages 77โ100):
Chapter 7 One?Dimensional Search Methods (pages 101โ123):
Chapter 8 Gradient Methods (pages 125โ153):
Chapter 9 Newton's Method (pages 155โ167):
Chapter 10 Conjugate Direction Methods (pages 169โ185):
Chapter 11 Quasi?Newton Methods (pages 187โ209):
Chapter 12 Solving Linear Equations (pages 211โ245):
Chapter 13 Unconstrained Optimization and Neural Networks (pages 247โ265):
Chapter 14 Global Search Algorithms (pages 267โ295):
Chapter 15 Introduction to Linear Programming (pages 297โ331):
Chapter 16 Simplex Method (pages 333โ370):
Chapter 17 Duality (pages 371โ393):
Chapter 18 Nonsimplex Methods (pages 395โ420):
Chapter 19 Problems with Equality Constraints (pages 421โ455):
Chapter 20 Problems with Inequality Constraints (pages 457โ477):
Chapter 21 Convex Optimization Problems (pages 479โ512):
Chapter 22 Algorithms for Constrained Optimization (pages 513โ539):
Chapter 23 Multiobjective Optimization (pages 541โ562):