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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.
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.
Keywords: linear optimization; nonlinear optimization; theory; algorithms; applications of optimization
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.
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 for 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: A Topics from Linear Algebra; B Other Fundamentals; C Software ; Bibliography; Index