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Newton-Type Methods for Optimization and Variational Problems (Springer Series in Operations Research and Financial Engineering) - Softcover
Synopsis
This book presents state-of-the-art theoretical analysis of fundamental Newtonian and Newtonian-related approaches to solving optimization and variational problems, and offers a set of tools for the unified treatment of various algorithms.
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From the Back Cover
This book presents comprehensive state-of-the-art theoretical analysis of the fundamental Newtonian and Newtonian-related approaches to solving optimization and variational problems. A central focus is the relationship between the basic Newton scheme for a given problem and algorithms that also enjoy fast local convergence. The authors develop general perturbed Newtonian frameworks that preserve fast convergence and consider specific algorithms as particular cases within those frameworks, i.e., as perturbations of the associated basic Newton iterations. This approach yields a set of tools for the unified treatment of various algorithms, including some not of the Newton type per se. Among the new subjects addressed is the class of degenerate problems. In particular, the phenomenon of attraction of Newton iterates to critical Lagrange multipliers and its consequences as well as stabilized Newton methods for variational problems and stabilized sequential quadratic programming for optimization. This volume will be useful to researchers and graduate students in the fields of optimization and variational analysis.
Review
“This book covers Newton-type methods (in a broad sense) for the solution of optimization and variational problems (like variational inequalities and complementarity problems). ... Several results presented in this book are new and based on recent publications, and cannot be found in any other monograph. ... a useful reference for researchers and graduate students working in the field of optimization and variational analysis.” (Christian Kanzow, Mathematical Reviews, July, 2015)
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- PublisherSpringer
- Publication date2016
- ISBN 10 3319353845
- ISBN 13 9783319353845
- BindingPaperback
- LanguageEnglish
- Number of pages592
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Newton-Type Methods for Optimization and Variational Problems
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ISBN 10: 3319353845
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Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -This book presents comprehensive state-of-the-art theoretical analysis of the fundamental Newtonian and Newtonian-related approaches to solving optimization and variational problems. A central focus is the relationship between the basic Newton scheme for a given problem and algorithms that also enjoy fast local convergence. The authors develop general perturbed Newtonian frameworks that preserve fast convergence and consider specific algorithms as particular cases within those frameworks, i.e., as perturbations of the associated basic Newton iterations. This approach yields a set of tools for the unified treatment of various algorithms, including some not of the Newton type per se. Among the new subjects addressed is the class of degenerate problems. In particular, the phenomenon of attraction of Newton iterates to critical Lagrange multipliers and its consequences as well as stabilized Newton methods for variational problems and stabilized sequential quadratic programming for optimization. This volume will be useful to researchers and graduate students in the fields of optimization and variational analysis. 596 pp. Englisch. Seller Inventory # 9783319353845
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Newton-Type Methods for Optimization and Variational Problems
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Taschenbuch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - This book presents comprehensive state-of-the-art theoretical analysis of the fundamental Newtonian and Newtonian-related approaches to solving optimization and variational problems. A central focus is the relationship between the basic Newton scheme for a given problem and algorithms that also enjoy fast local convergence. The authors develop general perturbed Newtonian frameworks that preserve fast convergence and consider specific algorithms as particular cases within those frameworks, i.e., as perturbations of the associated basic Newton iterations. This approach yields a set of tools for the unified treatment of various algorithms, including some not of the Newton type per se. Among the new subjects addressed is the class of degenerate problems. In particular, the phenomenon of attraction of Newton iterates to critical Lagrange multipliers and its consequences as well as stabilized Newton methods for variational problems and stabilized sequential quadratic programming for optimization. This volume will be useful to researchers and graduate students in the fields of optimization and variational analysis. Seller Inventory # 9783319353845
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Newton-Type Methods for Optimization and Variational Problems
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