Newton-Type Methods for Optimization and Variational Problems
Authors: Izmailov, Alexey F., Solodov, Mikhail V
Free Preview- Offers new approaches to optimization algorithms through Newtonian methods
- Relevant to researchers in Optimization and Variational Analysis
- Provides a unified view of classical as well as recent developments in the field of Newton-type methods
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- About this book
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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.
- Reviews
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“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)
- Table of contents (7 chapters)
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Elements of Optimization Theory and Variational Analysis
Pages 1-60
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Equations and Unconstrained Optimization
Pages 61-137
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Variational Problems: Local Methods
Pages 139-203
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Constrained Optimization: Local Methods
Pages 205-303
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Variational Problems: Globalization of Convergence
Pages 305-366
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Table of contents (7 chapters)
- Download Preface 1 PDF (59 KB)
- Download Sample pages 1 PDF (1 MB)
- Download Table of contents PDF (67.4 KB)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Newton-Type Methods for Optimization and Variational Problems
- Authors
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- Alexey F. Izmailov
- Mikhail V Solodov
- Series Title
- Springer Series in Operations Research and Financial Engineering
- Copyright
- 2014
- Publisher
- Springer International Publishing
- Copyright Holder
- Springer International Publishing Switzerland
- eBook ISBN
- 978-3-319-04247-3
- DOI
- 10.1007/978-3-319-04247-3
- Hardcover ISBN
- 978-3-319-04246-6
- Softcover ISBN
- 978-3-319-35384-5
- Series ISSN
- 1431-8598
- Edition Number
- 1
- Number of Pages
- XIX, 573
- Number of Illustrations
- 29 b/w illustrations, 1 illustrations in colour
- Topics
