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2014 | OriginalPaper | Buchkapitel

5. Variational Problems: Globalization of Convergence

verfasst von : Alexey F. Izmailov, Mikhail V. Solodov

Erschienen in: Newton-Type Methods for Optimization and Variational Problems

Verlag: Springer International Publishing

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Abstract

Newtonian methods for variational problems discussed in Chap. 3 have attractive local convergence and rate of convergence properties, but they are local by nature: for guaranteed convergence, they all require a starting point close enough to a solution. Therefore, to arrive to practical algorithms based on these methods, the process of computing and automatically accepting an appropriate “starting point” must be incorporated into the overall iterative scheme. Such extensions of locally convergent methods are referred to as globalization of convergence. This chapter discusses some strategies for globalization of convergence of Newtonian methods for variational problems.

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Titel: Variational Problems: Globalization of Convergence
verfasst von: Alexey F. Izmailov
Mikhail V. Solodov
Verlag: Springer International Publishing
Buch: Newton-Type Methods for Optimization and Variational Problems
Print ISBN: 978-3-319-04246-6

Electronic ISBN: 978-3-319-04247-3

Copyright-Jahr: 2014
DOI: https://doi.org/10.1007/978-3-319-04247-3_5