Seminário de Otimização & Problemas Inversos – 09/06/2023 às 14 horas
Seminário de Otimização & Problemas Inversos
Título: Inexact Newton regularizations with uniformly convex stability terms: a unified convergence analysis
Fábio Margotti (UFSC)
Resumo: We present a unified convergence analysis of inexact Newton regularizations for nonlinear ill-posed problems in Banach spaces. These schemes consist of an outer (Newton) iteration and an inner iteration which provides the update of the current outer iterate. To this end the nonlinear problem is linearized about the current iterate and the resulting linear system is approximately (inexactly) solved by an inner regularization method. In our analysis we only rely on generic assumptions of the inner methods and we show that a variety of regularization techniques satisfies these assumptions. For instance, gradient-type and iterated-Tikhonov methods are covered. Not only the technique of proof is novel, but also the results obtained, because for the first time uniformly convex penalty terms stabilize the inner scheme.
Palestrante: Fábio Margotti (UFSC)
Data: Segunda-feira, 19 de Junho , 14h
Local: Auditório Airton Silva do Departamento de Matemática
Maiores informações: http://mtm.ufsc.br/~maicon/seminar