Introduction to Optimization image
Introduction to Optimization Chong, Edwin K. P. Edition: 3rd 2008 Publisher: John Wiley & Sons, Incorporated Number of Pages: 608 ISBN10: 0471758000 ISBN13: 9780471758006 Dimensions: 6.42" w x 9.09" l x 1.36" h Weight: 2.07 lbs. Binding: Trade Cloth Language: English List Price: 122.00

Description

An Introduction to Optimization, Third Edition helps students build a solid working knowledge of the field, including unconstrained optimization, linear programming, and constrained optimization. The book is supplemented with numerous illustrations, an extensive bibliography, mathematical discussion at a level accessible to MBA and business students, a treatment of both linear and nonlinear progra...An Introduction to Optimization, Third Edition helps students build a solid working knowledge of the field, including unconstrained optimization, linear programming, and constrained optimization. The book is supplemented with numerous illustrations, an extensive bibliography, mathematical discussion at a level accessible to MBA and business students, a treatment of both linear and nonlinear programming, an introduction to recent developments such as neural networks and genetic algorithms, a chapter on the use of descent algorithms, and MATLAB exercises and examples.This authoritative book serves as an introductory text to optimization at the senior undergraduate and beginning graduate levels. With a consistently accessible and elementary treatment of all topics, An Introduction to Optimization, Third Edition helps students build a solid working knowledge of the field, including unconstrained optimization, linear programming, and constrained optimization. The book helps students prepare for the advanced topics and technological developments that lie ahead. It is also useful for researchers and professionals in mathematics, electrical engineering, economics, statistics, and business. The book is supplemented with numerous illustrations, an extensive bibliography, mathematical discussion at a level accessible to MBA and business students, a treatment of both linear and nonlinear programming, an introduction to recent developments such as neural networks and genetic algorithms, a chapter on the use of descent algorithms, and MATLAB exercises and examples. New to this edition: major topics such as the Nelder-Mead algorithm and the simulated annealing algorithm; a new chapter on multi-objective optimization, which discusses problems with multiple-objective functions and how they are treated, Pareto solutions, as well as algorithms for multi-objective problems, i.e. genetic algorithms; new references; and additional exercises.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 MATLABr 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.Praise from the Second Edition "...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 MATLABr 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.Preface. Part I: Mathematical Review. 1. Methods of Proof and Some Notation. 2. Vector Spaces and Matrices. 3. Transformations. 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. 17. Duality. 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. References. Index.Edwin K. P. Chong is Professor of Electrical and Computer Engineering and Professor of Mathematics at Colorado State University.Stanislaw H. Zak is Professor of Electrical and Computer Engineering at Purdue University."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."--BOOK JACKET. (more) (less)

Table of Contents

Preface
Mathematical Review
Methods of Proof and Some Notation
Methods of Proof
Notation
Exercises
Vector Spaces and Matrices
Vector and Matrix
Rank of a Matrix
Linear Equations
Inner Products and Norms
Exercises
Transformations
Linear Transformations
Eigenvalues and Eigenvectors
Orthogonal Projections
Quadratic Forms
Matrix Norms
Exercises
Concepts from Geometry
Line Segments
Hyperplanes and Linear Varieties
Convex Sets
Neighborhoods
Polytopes and Polyhedra
Exercises
Elements of Calculus
Sequences and Limits
Differentiability
The Derivative Matrix
Differentiation Rules
Level Sets and Gradients
Taylor Series
Exercises
Unconstrained Optimization
Basics of Set-Constrained and Unconstrained Optimization
Introduction
Conditions for Local Minimizers
Exercises
One-Dimensional Search Methods
Golden Section Search
Fibonacci Search
Newton's Method
Secant Method
Remarks on Line Search Methods
Exercises
Gradient Methods
Introduction
The Method of Steepest Descent
Analysis of Gradient Methods
Exercises
Newton's Method
Introduction
Analysis of Newton's Method
Levenberg-Marquardt Modification
Newton's Method for Nonlinear Least Squares
Exercises
Conjugate Direction Methods
Introduction
The Conjugate Direction Algorithm
The Conjugate Gradient Algorithm
The Conjugate Gradient Algorithm for Nonquadratic
Problems
Exercises
Quasi-Newton Methods
Introduction
Approximating the Inverse Hessian
The Rank One Correction Formula
The DFP Algorithm
The BFGS Algorithm
Exercises
Solving Linear Equations
Least-Squares Analysis
The Recursive Least-Squares Algorithm
Solution to a Linear Equation with Minimum Norm
Kaczmarz's Algorithm
Solving Linear Equations in General
Exercises
Unconstrained Optimization and Neural Networks
Introduction
Single-Neuron Training
The Backpropagation Algorithm
Exercises
Global Search Algorithms
Introduction
The Nelder-Mead Simplex Algorithm
Simulated Annealing
Particle Swarm Optimization
Genetic Algorithms
Exercises
Linear Programming
Introduction to Linear Programming
Brief History of Linear Programming
Simple Examples of Linear Programs
Two-Dimensional Linear Programs
Convex Polyhedra and Linear Programming
Standard Form Linear Programs
Basic Solutions
Properties of Basic Solutions
Geometric View of Linear Programs
Exercises
Simplex Method
Solving Linear Equations Using Row Operations
The Canonical Augmented Matrix
Updating the Augmented Matrix
The Simplex Algorithm
Matrix Form of the Simplex Method
Two-Phase Simplex Method
Revised Simplex Method
Exercises
Duality
Dual Linear Programs
Properties of Dual Problems
Exercises
Nonsimplex Methods
Introduction
Khachiyan's Method
Affine Scaling Method
Karmarkar's Method
Exercises
Nonlinear Constrained Optimization
Problems with Equality Constraints
Introduction
Problem Formulation
Tangent and Normal Spaces
Lagrange Condition
Second-Order Conditions
Minimizing Quadratics Subject to Linear Constraints
Exercises
Problems with Inequality Constraints
Karush-Kuhn-Tucker Condition
Second-Order Conditions
Exercises
Convex Optimization Problems
Introduction
Convex Functions
Convex Optimization Problems
Semidefinite Programming
Exercises
Algorithms for Constrained Optimization
Introduction
Projections
Projected Gradient Methods with Linear Constraints
Lagrangian Algorithms
Penalty Methods
Exercises
Multiobjective Optimization
Introduction
Pareto Solutions
Computing the Pareto Front
From Multiobjective to Single-Objective Optimization
Uncertain Linear Programming Problems
Exercises
References
Index

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