Linear and Nonlinear Optimization

2nd Edition

£77.00

textbook

Authors:
Igor Griva, George Mason University, Virginia
Stephen G. Nash, George Mason University, Virginia
Ariela Sofer, George Mason University, Virginia

Date Published: March 2009
availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
format: Hardback
isbn: 9780898716610

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Description

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.
- Supporting web site with data sets that are necessary for some of the book's exercises
- Three appendices on linear algebra, other fundamentals, and software packages for optimization problems
- Contains numerous examples and exercises to help the reader gain a deeper understanding
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Product details
- Edition: 2nd Edition
- Date Published: March 2009
- format: Hardback
- isbn: 9780898716610
- length: 764 pages
- dimensions: 261 x 181 x 37 mm
- weight: 1.49kg
- availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
Table of Contents
Preface
Part I. Basics:
1. Optimization models
2. Fundamentals of optimization
3. Representation of linear constraints
Part II. Linear Programming:
4. Geometry of linear programming
5. The simplex method
6. Duality and sensitivity
7. Enhancements of the simplex method
8. Network problems
9. Computational complexity of linear programming
10. Interior-point methods of linear programming
Part III. Unconstrained Optimization:
11. Basics of unconstrained optimization
12. Methods for unconstrained optimization
13. Low-storage methods for unconstrained problems
Part IV. Nonlinear Optimization:
14. Optimality conditions for constrained problems
15. Feasible-point methods
16. Penalty and barrier methods
Part V. Appendices: Appendix A. Topics from linear algebra
Appendix B. Other fundamentals
Appendix C. Software
Bibliography
Index.
Authors
Igor Griva, George Mason University, Virginia
Igor Griva received a B.Sc. and M.S. degree in applied mathematics in 1993 and 1994 from Moscow State University, Russia; and a Ph.D. in information technology in 2002 from George Mason University, where he is now an Assistant Professor of Computational Sciences and Mathematics in the College of Science. Prior to coming to George Mason University, he was a research associate at the Department of Financial Engineering and Operations Research in Princeton University. His research focuses on theory and methods of nonlinear optimization and their application to problems in science and engineering.
Stephen G. Nash, George Mason University, Virginia
Stephen Nash received a B.Sc. (Honors) degree in mathematics in 1977 from the University of Alberta, Canada; and a Ph.D. in computer science in 1982 from Stanford University. He is the Program Director for the Operations Research program at the National Science Foundation, on leave from George Mason University. Dr Nash is a Professor of Systems Engineering and Operations Research in the Volgenau School of Information Technology and Engineering. Prior to coming to George Mason University, he taught at The Johns Hopkins University. He has also had professional associations with the National Institute of Standards and Technology and the Argonne National Laboratory. His research activities are centered in scientific computing, especially nonlinear optimization, along with related interests in statistical computing and optimal control. He has been a member of the editorial boards of Computers in Science & Engineering, the SIAM Journal on Scientific Computing, Operations Research, and the Journal of the American Statistical Association.
Ariela Sofer, George Mason University, Virginia
Ariela Sofer received the B.Sc. in mathematics, and the M.Sc. in operations research from the Technion in Israel. She received the D.Sc. degree in operations research from the George Washington University in 1984. She 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. She has been a member of the editorial boards of the journals Operations Research and Management Science, and is coeditor on a subseries of the Annals of Operations Research on Operations Research in Medicine.