Local convergence of inexact Gauss-Newton like methods for injective-overdetermined systems of equations under a majorant condition

Local convergence of the Gauss-Newton method for injective-overdetermined systems of equations under a majorant condition

A local convergence analysis of the Gauss-Newton method for solving injective-overdetermined systems of nonlinear equations under a majorant condition is provided. The convergence as well as results on its rate are established without a convexity hypothesis on the derivative of the majorant function. The optimal convergence radius, the biggest range for uniqueness of the solution along with some other special cases are also obtained.range for uniqueness of the solution along with some other special cases.

Local convergence analysis of inexact Gauss-Newton like methods under majorant condition

In this paper, we present a local convergence analysis of inexact Gauss-Newton like methods for solving nonlinear least squares problems. Under the hypothesis that the derivative of the function associated with the least square problem satisfies a majorant condition, we obtain that the method is well-defined and converges. Our analysis provides a clear relationship between the majorant function and the function associated with the least square problem. It also allows us to obtain an estimate of convergence ball for inexact Gauss-Newton like methods and some important, special cases.

一阶majorization-minimization遇上高阶majorant：增强的非精确高阶前向-后向方法

First-order majorization-minimization meets high-order majorant: Boosted inexact high-order forward-backward method

本文提出基于高阶majorant的一阶majorization-minimization框架，开发了高阶非精确前向-后向算法（HiFBA）及其增强变体，在Kurdyka-Łojasiewicz条件下证明全局线性收敛，并在线性逆问题和NMF实验中展示高效性。

在主导条件下不精确牛顿类方法的局部收敛性分析

Local convergence analysis of inexact Newton-like methods under majorant condition

提出在主导条件下求解非线性方程的不精确牛顿类方法的局部收敛性分析，估计收敛半径并建立主导函数与非线性算子之间的关系。

An Inexact Newton-like conditional gradient method for constrained nonlinear systems

In this paper, we propose an inexact Newton-like conditional gradient method for solving constrained systems of nonlinear equations. The local convergence of the new method as well as results on its rate are established by using a general majorant condition. Two applications of such condition are provided: one is for functions whose the derivative satisfies Holder-like condition and the other is for functions that satisfies a Smale condition, which includes a substantial class of analytic functions. Some preliminaries numerical experiments illustrating the applicability of the proposed method …