Newton-type methods near critical solutions of piecewise smooth nonlinear equations

Fischer, A.; Izmailov, A.F.; Jelitte, M.

Статья опубликована в высокорейтинговом журнале

Информация о цитировании статьи получена из Scopus, Web of Science
Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 24 ноября 2021 г.

Авторы: Fischer A., Izmailov A.F., Jelitte M.
Журнал: Computational Optimization and Applications
Том: 80
Номер: 2
Год издания: 2021
Издательство: Springer Nature
Местоположение издательства: Switzerland
Первая страница: 587
Последняя страница: 615
DOI: 10.1007/s10589-021-00306-2
Аннотация: It is well-recognized that in the presence of singular (and in particular nonisolated) solutions of unconstrained or constrained smooth nonlinear equations, the existence of critical solutions has a crucial impact on the behavior of various Newton-type methods. On the one hand, it has been demonstrated that such solutions turn out to be attractors for sequences generated by these methods, for wide domains of starting points, and with a linear convergence rate estimate. On the other hand, the pattern of convergence to such solutions is quite special, and allows for a sharp characterization which serves, in particular, as a basis for some known acceleration techniques, and for the proof of an asymptotic acceptance of the unit stepsize. The latter is an essential property for the success of these techniques when combined with a linesearch strategy for globalization of convergence. This paper aims at extensions of these results to piecewise smooth equations, with applications to correspondingreformulations of nonlinear complementarity problems.
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