@article{0bb3199801a24d5dafa0bd6ab63d7d77,
title = "Convergence of a regularized Euclidean residual algorithm for nonlinear least-squares",
abstract = "The convergence properties of the new regularized Euclidean residual method for solving general nonlinear least-squares and nonlinear equation problems are investigated. This method, derived from a proposal by Nesterov [Optim. Methods Softw., 22 (2007), pp. 469-483], uses a model of the objective function consisting of the unsquared Euclidean linearized residual regularized by a quadratic term. At variance with previous analysis, its convergence properties are here considered without assuming uniformly nonsingular globally Lipschitz continuous Jacobians nor an exact sub-problem solution. It is proved that the method is globally convergent to first-order critical points and, under stronger assumptions, to roots of the underlying system of nonlinear equations. The rate of convergence is also shown to be quadratic under stronger assumptions. {\textcopyright} 2010 Society for Industrial and Applied Mathematics.",
keywords = " numerical algorithms, systems of nonlinear equations, Nonlinear least-squares, global convergence.",
author = "S. Bellavia and B. Morini and C. Cartis and N.I.M. Gould and Ph.L. Toint",
note = "Publication code : FP SB10/2008/11 ; QA 0002.2/001/08/11",
year = "2010",
month = jan,
day = "1",
doi = "10.1137/080732432",
language = "English",
volume = "48",
pages = "1--29",
journal = "SIAM Journal on Numerical Analysis",
issn = "1095-7170",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "1",
}