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Related papers: Continuous analog of Gauss-Newton method

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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…

Optimization and Control · Mathematics 2011-03-03 Saverio Salzo , Silvia Villa

A new continuous regularized Gauss-Newton-type method with simultaneous updates of the operator $(F^{\pr*}(x(t))F'(x(t))+\ep(t) I)^{-1}$ for solving nonlinear ill-posed equations in a Hilbert space is proposed. A convergence theorem is…

Mathematical Physics · Physics 2007-05-23 Alexander G. Ramm , Alexandra B. Smirnova

In this paper we consider the iteratively regularized Gauss-Newton method for solving nonlinear ill-posed inverse problems. Under merely Lipschitz condition, we prove that this method together with an a posteriori stopping rule defines an…

Numerical Analysis · Mathematics 2009-11-13 Qinian Jin

A general method for solving nonlinear ill-posed problems is developed. The method consists of solving a Cauchy problem with a regularized operator and proving that the solution of this problem tends, as time grows, to a solution of the…

Mathematical Physics · Physics 2007-05-23 R. Airapetyan , A. G. Ramm , A. Smirnova

A q-Gauss-Newton algorithm is an iterative procedure that solves nonlinear unconstrained optimization problems based on minimization of the sum squared errors of the objective function residuals. Main advantage of the algorithm is that it…

Optimization and Control · Mathematics 2021-05-28 Danijela Protic , Miomir Stankovic

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…

Optimization and Control · Mathematics 2013-03-21 Max Leandro Nobre Goncalves

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…

Optimization and Control · Mathematics 2020-12-08 Ilyes Mezghani , Quoc Tran-Dinh , Ion Necoara , Anthony Papavasiliou

This work presents a novel version of recently developed Gauss-Newton method for solving systems of nonlinear equations, based on upper bound of solution residual and quadratic regularization ideas. We obtained for such method global…

Optimization and Control · Mathematics 2021-05-04 Nikita Yudin , Alexander Gasnikov

This paper addresses the challenge of solving large-scale nonlinear equations with H\"older continuous Jacobians. We introduce a novel Incremental Gauss--Newton (IGN) method within explicit superlinear convergence rate, which outperforms…

Optimization and Control · Mathematics 2024-07-04 Zhiling Zhou , Zhuanghua Liu , Chengchang Liu , Luo Luo

Gauss-Newton methods and their stochastic version have been widely used in machine learning and signal processing. Their nonsmooth counterparts, modified Gauss-Newton or prox-linear algorithms, can lead to contrasting outcomes when compared…

Optimization and Control · Mathematics 2023-05-19 Krishna Pillutla , Vincent Roulet , Sham Kakade , Zaid Harchaoui

As second-order methods, Gauss--Newton-type methods can be more effective than first-order methods for the solution of nonsmooth optimization problems with expensive-to-evaluate smooth components. Such methods, however, often do not…

Optimization and Control · Mathematics 2020-09-01 Jyrki Jauhiainen , Petri Kuusela , Aku Seppänen , Tuomo Valkonen

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…

Optimization and Control · Mathematics 2025-04-02 Yassine Nabou , Lucian Toma , Ion Necoara

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…

Optimization and Control · Mathematics 2010-08-12 O. P. Ferreira , M. L. N. Goncalves , P. R. Oliveira

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…

Numerical Analysis · Mathematics 2019-11-01 Dario Fasino , Antonio Fazzi

In this paper, we propose a globally convergent method for solving constrained nonlinear systems. The method combines an efficient Newton conditional gradient method with a derivative-free and nonmonotone linesearch strategy. The global…

Optimization and Control · Mathematics 2018-06-06 M. L. N. Gonçalves , F. R. Oliveira

The present work deals with an improved back-propagation algorithm based on Gauss-Newton numerical optimization method for fast convergence. The steepest descent method is used for the back-propagation. The algorithm is tested using various…

Artificial Intelligence · Computer Science 2012-06-21 Sudarshan Nandy , Partha Pratim Sarkar , Achintya Das

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…

Optimization and Control · Mathematics 2010-03-29 O. P. Ferreira , M. L. N. Goncalves , P. R. Oliveira

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…

Numerical Analysis · Mathematics 2021-09-20 Federica Pes , Giuseppe Rodriguez

In this paper, we introduce an iterative numerical method to solve systems of nonlinear equations. The third-order convergence of this method is analyzed. Several examples are given to illustrate the efficiency of the proposed method.

Dynamical Systems · Mathematics 2009-04-23 M. Eshaghi Gordji , A. Ebadian , M. B. Ghaemi , J. Shokri

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…

Optimization and Control · Mathematics 2019-03-06 Mou Wu , Naixue Xiong , Liansheng Tan
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