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In this paper, we introduce a Gauss-Newton method for solving the complex phase retrieval problem. In contrast to the real-valued setting, the Gauss-Newton matrix for complex-valued signals is rank-deficient and, thus, non-invertible. To…

Numerical Analysis · Mathematics 2024-06-17 Meng Huang

In this manuscript, we propose a general proximal quasi-Newton method tailored for nonconvex and nonsmooth optimization problems, where we do not require the sequence of the variable metric (or Hessian approximation) to be uniformly bounded…

Optimization and Control · Mathematics 2025-07-28 Xiaoxi Jia

In this paper, we propose a structure-guided Gauss-Newton (SgGN) method for solving least squares problems using a shallow ReLU neural network. The method effectively takes advantage of both the least squares structure and the neural…

Machine Learning · Computer Science 2025-07-22 Zhiqiang Cai , Tong Ding , Min Liu , Xinyu Liu , Jianlin Xia

The weighted nonlinear least-squares problem for low-rank signal estimation is considered. The problem of constructing a numerical solution that is stable and fast for long time series is addressed. A modified weighted Gauss-Newton method,…

Numerical Analysis · Mathematics 2022-07-08 Nikita Zvonarev , Nina Golyandina

We consider the problem of minimizing a continuous function that may be nonsmooth and nonconvex, subject to bound constraints. We propose an algorithm that uses the L-BFGS quasi-Newton approximation of the problem's curvature together with…

Optimization and Control · Mathematics 2016-12-23 Nitish Shirish Keskar , Andreas Waechter

Consider the problem of estimating the mean of a Gaussian random vector when the mean vector is assumed to be in a given convex set. The most natural solution is to take the Euclidean projection of the data vector on to this convex set; in…

Statistics Theory · Mathematics 2014-11-21 Sourav Chatterjee

An inexact Newton type method for numerical minimization of convex piecewise quadratic functions is considered and its convergence is analyzed. Earlier, a similar method was successfully applied to optimizaton problems arising in numerical…

Optimization and Control · Mathematics 2019-01-11 Alexander I. Golikov , Igor E. Kaporin

Variable projection methods prove highly efficient in solving separable nonlinear least squares problems by transforming them into a reduced nonlinear least squares problem, typically solvable via the Gauss-Newton method. When solving…

Numerical Analysis · Mathematics 2024-02-14 Malena I. Español , Gabriela Jeronimo

We propose a general random subspace framework for unconstrained nonconvex optimization problems that requires a weak probabilistic assumption on the subspace gradient, which we show to be satisfied by various random matrix ensembles, such…

Optimization and Control · Mathematics 2022-11-21 Coralia Cartis , Jaroslav Fowkes , Zhen Shao

We develop and analyze stochastic inexact Gauss-Newton methods for nonlinear least-squares problems and for nonlinear systems ofequations. Random models are formed using suitable sampling strategies for the matrices involved in the…

Optimization and Control · Mathematics 2024-12-10 Stefania Bellavia , Greta Malaspina , Benedetta Morini

We present a stochastic inexact Gauss-Newton method for the solution of nonlinear least-squares. To reduce the computational cost with respect to the classical method, at each iteration the proposed algorithm approximately minimizes the…

Optimization and Control · Mathematics 2025-06-05 Stefania Bellavia , Greta Malaspina , Benedetta Morini

We propose a communication- and computation-efficient distributed optimization algorithm using second-order information for solving ERM problems with a nonsmooth regularization term. Current second-order and quasi-Newton methods for this…

Optimization and Control · Mathematics 2018-05-29 Ching-pei Lee , Cong Han Lim , Stephen J. Wright

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

This paper introduces a smoothed proximal Lagrangian method for minimizing a nonconvex smooth function over a convex domain with additional explicit convex nonlinear constraints. Two key features are 1) the proposed method is single-looped,…

Optimization and Control · Mathematics 2024-08-28 Wenqiang Pu , Kaizhao Sun , Jiawei Zhang

Motivated by variational models in continuum mechanics, we introduce a novel algorithm to perform nonsmooth and nonconvex minimizations with linear constraints in Euclidean spaces. We show how this algorithm is actually a natural…

Analysis of PDEs · Mathematics 2015-03-20 Marco Artina , Massimo Fornasier , Francesco Solombrino

This paper extends the SQP-approach of the well-known bundle-Newton method for nonsmooth unconstrained minimization to the nonlinearly constrained case. Instead of using a penalty function or a filter or an improvement function to deal with…

Optimization and Control · Mathematics 2015-06-29 Hannes Fendl , Hermann Schichl

We propose a stochastic variance-reduced cubic regularized Newton method for non-convex optimization. At the core of our algorithm is a novel semi-stochastic gradient along with a semi-stochastic Hessian, which are specifically designed for…

Machine Learning · Computer Science 2018-02-14 Dongruo Zhou , Pan Xu , Quanquan Gu

This paper describes an extension of the BFGS and L-BFGS methods for the minimization of a nonlinear function subject to errors. This work is motivated by applications that contain computational noise, employ low-precision arithmetic, or…

Optimization and Control · Mathematics 2021-09-10 Hao-Jun Michael Shi , Yuchen Xie , Richard Byrd , Jorge Nocedal

Optimization problems with composite functions consist of an objective function which is the sum of a smooth and a (convex) nonsmooth term. This particular structure is exploited by the class of proximal gradient methods and some of their…

Optimization and Control · Mathematics 2022-10-17 Christian Kanzow , Theresa Lechner

Nonlinear regression analysis is a popular and important tool for scientists and engineers. In this article, we introduce theories and methods of nonlinear regression and its statistical inferences using the frequentist and Bayesian…

Methodology · Statistics 2024-02-09 Hsin-Hsiung Huang , Qing He