相关论文: Local convergence analysis of a proximal Gauss-New…
The Gauss-Newton's method for solving nonlinear least squares problems is studied in this paper. Under the hypothesis that the derivative of the function associated with the least square problem satisfies a majorant condition, a local…
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…
An extension of the Gauss-Newton algorithm is proposed to find local minimizers of penalized nonlinear least squares problems, under generalized Lipschitz assumptions. Convergence results of local type are obtained, as well as an estimate…
In this paper, we study the Gauss-Newton method for a special class of systems of nonlinear equation. Under the hypothesis that the derivative of the function under consideration satisfies a majorant condition, semi-local convergence…
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…
Under the hypothesis that an initial point is a quasi-regular point, we use a majorant condition to present a new semi-local convergence analysis of an extension of the Gauss-Newton method for solving convex composite optimization problems.…
In this paper, inexact Gauss-Newton like methods for solving injective-overdetermined systems of equations are studied. We use a majorant condition, defined by a function whose derivative is not necessarily convex, to extend and improve…
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 convergence radius and a clear relationship between the majorant…
We present a local convergence analysis of the Gauss-Newton-Kurchatov method for solving nonlinear least squares problems with a decomposition of the operator. The method uses the sum of the derivative of the differentiable part of the…
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 derivative of the majorant function, which relaxes the Lipschitz…
We obtain estimates of the multiplicative constants appearing in local convergence results of the Riemannian Gauss-Newton method for least squares problems on manifolds and relate them to the geometric condition number of [P. B\"urgisser…
The Total Least Squares solution of an overdetermined, approximate linear equation $Ax \approx b$ minimizes a nonlinear function which characterizes the backward error. We show that a globally convergent variant of the Gauss--Newton…
When a physical system is modeled by a nonlinear function, the unknown parameters can be estimated by fitting experimental observations by a least-squares approach. Newton's method and its variants are often used to solve problems of this…
In this paper, we consider a modified projected Gauss-Newton method for solving constrained nonlinear least-squares problems. We assume that the functional constraints are smooth and the the other constraints are represented by a simple…
In this paper we study Newton's method for solving the generalized equation $F(x)+T(x)\ni 0$ in Hilbert spaces, where $F$ is a Fr\'echet differentiable function and $T$ is set-valued and maximal monotone. We show that this method is local…
We propose a globally convergent Gauss-Newton algorithm for finding a local optimal solution of a non-convex and possibly non-smooth optimization problem. The algorithm that we present is based on a Gauss-Newton-type iteration for the…
In this paper we generalize the technique of deflation to define two new methods to systematically find many local minima of a nonlinear least squares problem. The methods are based on the Gauss-Newton algorithm, and as such do not require…
In this paper, we investigate the convergence performance of a cooperative diffusion Gauss-Newton (GN) method, which is widely used to solve the nonlinear least squares problems (NLLS) due to the low computation cost compared with Newton's…
A local convergence rate is established for an orthogonal collocation method based on Gauss quadrature applied to an unconstrained optimal control problem. If the continuous problem has a sufficiently smooth solution and the Hamiltonian…
The proximal gradient algorithm for minimizing the sum of a smooth and a nonsmooth convex function often converges linearly even without strong convexity. One common reason is that a multiple of the step length at each iteration may…