Linear and Nonlinear Optimization

by Griva, Igor; Nash, Stephen G.; Sofer, Ariela

• ISBN13: 9780898716610
• ISBN10: 0898716616
• Edition: 2nd
• Format: Hardcover
• Copyright: 2012-04-30
• Publisher: Society for Industrial & Applied
• More Book Details

Summary

Provides an introduction to the applications, theory, and algorithms of linear and nonlinear optimization. The emphasis is on practical aspects - discussing modern algorithms, as well as the influence of theory on the interpretation of solutions or on the design of software. The book includes several examples of realistic optimization models that address important applications. The succinct style of this second edition is punctuated with numerous real-life examples and exercises, and the authors include accessible explanations of topics that are not often mentioned in textbooks, such as duality in nonlinear optimization, primal-dual methods for nonlinear optimization, filter methods, and applications such as support-vector machines. The book is designed to be flexible. It has a modular structure, and uses consistent notation and terminology throughout. It can be used in many different ways, in many different courses, and at many different levels of sophistication.

Author Biography

Igor Griva is an Assistant Professor in the Department of Computational and Data Science and the Department of Mathematical Sciences at George Mason University. His research focuses on the theory and methods of nonlinear optimization and their application to problems in science and engineering.Stephen G. Nash is a Professor of Systems Engineering and Operations Research at George Mason University. His research focuses on scientific computing, especially nonlinear optimization, along with related interests in statistical computing and optimal control.Ariela Sofer is Professor and Chair of the Systems Engineering and Operations Research Department at George Mason University. Her major areas of interest are nonlinear optimization and optimization in biomedical applications.

Table of Contents

Preface

Basics

Optimization models

Fundamentals of optimization

Representation of linear constraints

Linear Programming:

Geometry of linear programming

The simplex method

Duality and sensitivity

Enhancements of the simplex method

Network problems

Computational complexity of linear programming

Interior-point methods of linear programming

Unconstrained Optimization

Basics of unconstrained optimization

Methods for unconstrained optimization

Low-storage methods for unconstrained problems

Nonlinear Optimization

Optimality conditions for constrained problems

Feasible-point methods

Penalty and barrier methods

Appendices

Topics from linear algebra

Other fundamentals

Software

Bibliography

Index

Table of Contents provided by Publisher. All Rights Reserved.