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The paper contains several theoretical results related to the weighted nonlinear least-squares problem for low-rank signal estimation, which can be considered as a Hankel structured low-rank approximation problem. A parameterization of the…

Numerical Analysis · Mathematics 2022-07-29 Nikita Zvonarev , Nina Golyandina

In this paper, we propose a stochastic Gauss-Newton (SGN) algorithm to study the online principal component analysis (OPCA) problem, which is formulated by using the symmetric low-rank product (SLRP) model for dominant eigenspace…

Optimization and Control · Mathematics 2022-10-25 Siyun Zhou , Xin Liu , Liwei Xu

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

In this paper, we consider the estimation of a low Tucker rank tensor from a number of noisy linear measurements. The general problem covers many specific examples arising from applications, including tensor regression, tensor completion,…

Machine Learning · Statistics 2023-07-11 Yuetian Luo , Anru R. Zhang

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

This work focuses on developing and motivating a stochastic version of a wellknown inverse problem methodology. Specifically, we consider the iteratively regularized Gauss-Newton method, originally proposed by Bakushinskii for…

Numerical Analysis · Mathematics 2024-09-20 El Houcine Bergou , Neil K. Chada , Youssef Diouane

We present an algorithm for minimizing a sum of functions that combines the computational efficiency of stochastic gradient descent (SGD) with the second order curvature information leveraged by quasi-Newton methods. We unify these…

Machine Learning · Computer Science 2014-12-02 Jascha Sohl-Dickstein , Ben Poole , Surya Ganguli

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

Non linear regression models are a standard tool for modeling real phenomena, with several applications in machine learning, ecology, econometry... Estimating the parameters of the model has garnered a lot of attention during many years. We…

Statistics Theory · Mathematics 2020-09-17 Peggy Cénac , Antoine Godichon-Baggioni , Bruno Portier

The paper is devoted to the solution of a weighted nonlinear least-squares problem for low-rank signal estimation, which is related to Hankel structured low-rank approximation problems. A modified weighted Gauss-Newton method, which uses…

Numerical Analysis · Mathematics 2020-12-01 N. Zvonarev , N. Golyandina

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

Following early work on Hessian-free methods for deep learning, we study a stochastic generalized Gauss-Newton method (SGN) for training DNNs. SGN is a second-order optimization method, with efficient iterations, that we demonstrate to…

Machine Learning · Computer Science 2020-06-11 Matilde Gargiani , Andrea Zanelli , Moritz Diehl , Frank Hutter

We consider the numerical solution of parameterized linear systems where the system matrix, the solution, and the right-hand side are parameterized by a set of uncertain input parameters. We explore spectral methods in which the solutions…

Numerical Analysis · Mathematics 2017-01-09 Kookjin Lee , Kevin Carlberg , Howard C. Elman

In signal processing and data recovery, reconstructing a signal from quadratic measurements poses a significant challenge, particularly in high-dimensional settings where measurements $m$ is far less than the signal dimension $n$ (i.e., $m…

Information Theory · Computer Science 2025-07-11 Jinming Wen , Yi Hu , Meng Huang

The generalized Gauss-Newton (GGN) optimization method incorporates curvature estimates into its solution steps, and provides a good approximation to the Newton method for large-scale optimization problems. GGN has been found particularly…

Machine Learning · Computer Science 2024-04-24 Adeyemi D. Adeoye , Philipp Christian Petersen , Alberto Bemporad

We study nonlinear constrained optimization problems in which only function evaluations of the objective and constraints are available. Existing zeroth-order methods rely on noisy gradient and Jacobian surrogates in high dimensions, making…

Optimization and Control · Mathematics 2026-04-03 Runyu Zhang , Gioele Zardini

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

In this paper, we propose a new randomized second-order optimization algorithm---Stochastic Subspace Cubic Newton (SSCN)---for minimizing a high dimensional convex function $f$. Our method can be seen both as a {\em stochastic} extension of…

Optimization and Control · Mathematics 2020-02-25 Filip Hanzely , Nikita Doikov , Peter Richtárik , Yurii Nesterov

We propose a new globally convergent stochastic second order method. Our starting point is the development of a new Sketched Newton-Raphson (SNR) method for solving large scale nonlinear equations of the form $F(x)=0$ with $F:\mathbb{R}^p…

Numerical Analysis · Mathematics 2022-05-10 Rui Yuan , Alessandro Lazaric , Robert M. Gower

We propose an abstract discontinuous Galerkin neural network (DGNN) framework for analyzing the convergence of least-squares methods based on the residual minimization when feasible solutions are neural networks. Within this framework, we…

Numerical Analysis · Mathematics 2025-11-11 Long Yuan , Hongxing Rui