Linear and Nonlinear Optimization / Edition 2

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

Overview

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.

Product Details

ISBN-13:	9780898716610
Publisher:	SIAM
Publication date:	02/28/2009
Edition description:	New Edition
Pages:	768
Product dimensions:	6.85(w) x 9.72(h) x 1.46(d)

About the Author

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 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 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.

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.