8 citations · 29 across the 50 of their papers we have counts for
13 papers · 1 filter
Newton's Method with GeoGebra
Orizon P. Ferreira, Davi A. Pires
In this work, we present a program in the computational environment, GeoGebra, that enables a graphical study of Newton's Method. Using this computational device, we will analyze N…
On the globalization of Riemannian Newton method
Marcio Antonio de Andrade Bortoloti, Teles Araujo Fernandes, Orizon Pereira Ferreira
In the present paper, in order to fnd a singularity of a vector field defined on Riemannian manifolds, we present a new globalization strategy of Newton method and establish its gl…
Iteration-complexity of gradient, subgradient and proximal point methods on Riemannian manifolds
G. C. Bento, O. P. Ferreira, J. G. Melo
This paper considers optimization problems on Riemannian manifolds and analyzes iteration-complexity for gradient and subgradient methods on manifolds with non-negative curvature.…
Kantorovich's theorem on Newton's method for solving strongly regular generalized equation
O. P. Ferreira, G. N. Silva
In this paper we consider the Newton's method for solving the generalized equation of the form where is a continuously differentiable mapping, …
Local convergence analysis of Newton's method for solving strongly regular generalized equations
O. P. Ferreira, G. N. Silva
In this paper we study Newton's method for solving generalized equations in Banach spaces. We show that under strong regularity of the generalized equation, the method is locally c…
Inexact Newton's method to nonlinear functions with values in a cone
O. P. Ferreira, G. N. Silva
The problem of finding a solution of nonlinear inclusion problems in Banach space is considered in this paper. Using convex optimization techniques introduced by Robinson (Numer. M…
A robust semi-local convergence analysis of Newton's method for cone inclusion problems in Banach spaces under affine invariant majorant condition
Orizon P Ferreira
A semi-local analysis of Newton's method for solving nonlinear inclusion problems in Banach space is presented in this paper. Under a affine majorant condition on the nonlinear fun…
Local convergence analysis of Inexact Newton method with relative residual error tolerance under majorant condition in Riemannian Manifolds
T. Bittencourt, O. P. Ferreira
A local convergence analysis of Inexact Newton's method with relative residual error tolerance for finding a singularity of a differentiable vector field defined on a complete Riem…
Kantorovich's Theorem on Newton's Method
O. P. Ferreira, B. F. Svaiter
In this work we present a simplifyed proof of Kantorovich's Theorem on Newton's Method. This analysis uses a technique which has already been used for obtaining new extensions of t…
A robust Kantorovich's theorem on inexact Newton method with relative residual error tolerance
O. P. Ferreira, B. F. Svaiter
We prove that under semi-local assumptions, the inexact Newton method with a fixed relative residual error tolerance converges Q-linearly to a zero of the non-linear operator under…
Unconstrained steepest descent method for multicriteria optimization on Riemmanian manifolds
G. C. Bento, O. P. Ferreira, P. R. Oliveira
In this paper we present a steepest descent method with Armijo's rule for multicriteria optimization in the Riemannian context. The well definedness of the sequence generated by th…
Local convergence of Newton's method under majorant condition
O. P. Ferreira
A local convergence analysis of Newton's method for solving nonlinear equations, under a majorant condition, is presented in this paper. Without assuming convexity of the derivativ…
Local convergence analysis of inexact Newton-like methods under majorant condition
O. P. Ferreira, M. L. N. Goncalves
We present a local convergence analysis of inexact Newton-like methods for solving nonlinear equations under majorant conditions. This analysis provides an estimate of the converge…