Linear and Nonlinear Optimization, Second Edition
By Igor Griva, Stephen G. Nash, Ariela Sofer
* Publisher: Society for Industrial and Applied Mathematics
* Number Of Pages: 764
* Publication Date: 2008-12-03
* ISBN-10 / ASIN: 0898716616
* ISBN-13 / EAN: 9780898716610
Product Description
This book introduces the applications, theory, and algorithms of linear and nonlinear optimization, with an emphasis on the practical aspects of the material. Its unique modular structure provides flexibility to accommodate the varying needs of instructors, students, and practitioners with different levels of sophistication in these topics. 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.
Part I of Linear and Nonlinear Optimization, Second Edition provides fundamentals that can be taught in whole or in part at the beginning of a course on either topic and then referred to as needed. Part II on linear programming and Part III on unconstrained optimization can be used together or separately, and Part IV on nonlinear optimization can be taught without having studied the material in Part II. In the preface the authors suggest course outlines that can be adjusted to the requirements of a particular course on both linear and nonlinear optimization, or to separate courses on these topics. Three appendices provide information on linear algebra, other fundamentals, and software packages for optimization problems. A supplemental website offers auxiliary data sets that are necessary for some of the exercises.
Audience: This book is primarily intended for use in linear and nonlinear optimization courses for advanced undergraduate and graduate students. It is also appropriate as a tutorial for researchers and practitioners who need to understand the modern algorithms of linear and nonlinear optimization to apply them to problems in science and engineering.
Contents:
Preface
Part I: Basics
Chapter 1: Optimization Models
Chapter 2: Fundamentals of Optimization
Chapter 3: Representation of Linear Constraints
Part II: Linear Programming
Chapter 4: Geometry of Linear Programming
Chapter 5: The Simplex Method
Chapter 6: Duality and Sensitivity
Chapter 7: Enhancements of the Simplex Method
Chapter 8: Network Problems
Chapter 9: Computational Complexity of Linear Programming
Chapter 10: Interior-Point Methods of Linear Programming
Part III: Unconstrained Optimization
Chapter 11: Basics of Unconstrained Optimization
Chapter 12: Methods for Unconstrained Optimization
Chapter 13: Low-Storage Methods for Unconstrained Problems
Part IV: Nonlinear Optimization
Chapter 14: Optimality Conditions for Constrained Problems
Chapter 15: Feasible-Point Methods
Chapter 16: Penalty and Barrier Methods
Part V: Appendices
Appendix A: Topics from Linear Algebra
Appendix B: Other Fundamentals
Appendix C: Software
Bibliography
Index
Book Description
Flexible graduate textbook that introduces the applications, theory, and algorithms of linear and nonlinear optimization in a clear succinct style, supported by numerous examples and exercises. It introduces important realistic applications and explains how optimization can address them.
About the Authors
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.
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