Practical quasi-Newton methods for solving nonlinear systems are surveyed. The definition
of quasi-Newton methods that includes Newton's method as a particular case is adopted …

The spectral gradient method has proved to be effective for solving large-scale optimization
problems. In this work we extend the spectral approach to solve nonlinear systems of …

In this paper, a conjugate gradient algorithm for systems of large-scale nonlinear equations
is designed by the following steps:(i) A three-terms conjugate gradient direction dk is …

This paper investigates inexact Newton methods for solving systems of nonsmooth
equations. We define two inexact Newton methods for locally Lipschitz functions and we …

This paper proposes a class of randomized Kaczmarz algorithms for obtaining isolated
solutions of large-scale well-posed or overdetermined nonlinear systems of equations. This …

Recently, a class of nonlinear Kaczmarz (NK) algorithms has been proposed to solve large-
scale nonlinear systems of equations. The NK algorithm is a generalization of the Newton …

In this paper, we propose a fast inertial self-adaptive projection based algorithm for solving
large-scale monotone equations with the relaxation factor. The modified hyperplane …

Otimizaçao é um problema matemático com muitas aplicaçoes no “mundo real”. Consiste
em encontrar os mınimos ou máximos de uma funçao de várias variáveis, com valores …

The main purpose of this paper is to prove the global convergence of the new trust region
method based on the smoothed CGS algorithm. This method is surprisingly convenient for …

I describe an algorithm for simultaneous fixed-point optimization (mixing) of the density and
atomic positions in Density Functional Theory calculations which is approximately twice as …