Newton-Type Methods for Optimization and Variational Problems (Springer Series in Operations Research and Financial Engineering) - Hardcover

Izmailov, Alexey F.; Solodov, Mikhail V.

 
9783319042466: Newton-Type Methods for Optimization and Variational Problems (Springer Series in Operations Research and Financial Engineering)
Hardcover
ISBN 10: 3319042467 ISBN 13: 9783319042466
Publisher: Springer, 2014

Synopsis

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.

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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.

"About this title" may belong to another edition of this title.

Publisher
Springer
Publication date
2014
Language
English
ISBN 10 
3319042467
ISBN 13 
9783319042466
Binding
Hardcover
Number of pages
592

Other Popular Editions of the Same Title

9783319353845: Newton-Type Methods for Optimization and Variational Problems (Springer Series in Operations Research and Financial Engineering)

Featured Edition

ISBN 10:  3319353845 ISBN 13:  9783319353845
Publisher: Springer, 2016
Softcover