Seminários de Otimização – 31/08/2018 10h:30m

30/08/2018 19:43

Seminários de Otimização

Local convergence of Levenberg-Marquardt methods for nonzero-residue nonlinear least-squares problems under an error bound condition

Expositor: Douglas S. Gonçalves (UFSC)

Resumo: The Levenberg-Marquardt method (LM) is widely used for solving nonlinear systems of equations, as well as nonlinear least-squares problems. In this study, we consider local convergence issues of the LM method when applied to nonzero-residue nonlinear least-squares problems under an error bound condition, which is weaker than requiring full-rank of the Jacobian in a neighborhood of a stationary point. Differently from the zero-residue case, the choice of the LM parameter is shown to be dictated by (i)~the behavior of the rank of the Jacobian, and (ii)~a combined measure of nonlinearity and residue size in a neighborhood of the set of (possibly non-isolated) stationary points of the sum of squares function.

Data: Sexta-feira, 31 de agosto, 10h30m
Local: Auditório Airton Silva, sala MTM007 do Departamento de Matemática.

Maiores informações:

E. Krukoski
Tags: least-squares problemsLevenberg-MarquardtLM methodnonlinearnonzero-residueotimizaçãoSeminários

Seminario de Matematica Aplicada – 07/07/2016

05/07/2016 12:56

Seminario de Matematica Aplicada

On a family of gradient type projection methods for nonlinear ill-posed problems

Prof. Dr. Antonio C. G. Leitão – MTM/UFSC


Resumo: We propose and analyze a family of successive projection methods whose step direction is the same as Landweber method for solving nonlinear ill-posed problems that satisfy the Tangential Cone Condition (TCC). This family encompasses Landweber method, the minimal error method, and the steepest descent method; thus providing an unified framework for the analysis of these methods. Moreover, we define in this family new methods which are convergent for the constant of the TCC in a range twice as large as the one required for the Landweber and other gradient type methods.

Dia – Hora: 07/07/2016 – 15:00 h
Local: Auditório Departamento de Matemática, MTM 007, CFM/UFSC



E. Krukoski
Tags: ill-posed problemsMatematica AplicadanonlinearSeminario