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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.
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
Fundamentals of optimization
Representation of linear constraints
Geometry of linear programming
The simplex method
Duality and sensitivity
Enhancements of the simplex method
Computational complexity of linear programming
Interior-point methods of linear programming
Basics of unconstrained optimization
Methods for unconstrained optimization
Low-storage methods for unconstrained problems
Optimality conditions for constrained problems
Penalty and barrier methods
Topics from linear algebra
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