The effect of calmness on the solution set of systems of nonlinear equations
type: Item
instance of: scholarly article
title: The effect of calmness on the solution set of systems of nonlinear equations
zbMATH Open document ID: 1266.65079
author: Roger Behling
author: Alfredo Iusem
published in: Mathematical Programming. Series A. Series B
publication date: 2013-03-18T00:00:00Z
review text: The authors address the problem of solving a system of continuously differentiable nonlinear equations under the condition of calmness (also called upper Lipschitz-continuity). The notion of calmness is quite useful in the study of the convergence properties of iterative methods and also has implications in connection with Karush-Kuhn-Tucker (KKT) systems. In this paper, the authors prove that the local error bound described by calmness, together with the continuous differentiability, imply that the rank of the Jacobian is locally constant on the solution set. They also prove that locally, the solution set must be a differentiable manifold.
Mathematics Subject Classification ID: 65H10
zbMATH DE Number: 6145967
zbMATH Keywords: calmness
zbMATH Keywords: upper Lipschitz-continuity
zbMATH Keywords: local error bound
zbMATH Keywords: Levenberg-Marquardt method
zbMATH Keywords: system of nonlinear equations
zbMATH Keywords: convergence
zbMATH Keywords: iterativ methods
zbMATH Keywords: Karush-Kuhn-Tucker systems
reviewed by: Liu Xinguo
describes a project that uses: levmar
MaRDI profile type: Publication
full work available at URL: s10107-011-0486-7
OpenAlex ID: W2006963158
cites work: Convergence Properties of the Inexact Levenberg-Marquardt Method under Local Error Bound Conditions
cites work: Q4348513
cites work: Inexact Levenberg-Marquardt method for nonlinear equations
cites work: On the quadratic convergence of the Levenberg-Marquardt method without nonsingularity assumption
cites work: Local behavior of an iterative framework for generalized equations with nonisolated solutions
cites work: A Levenberg-Marquardt algorithm for unconstrained multicriteria optimization
cites work: On the inexactness level of robust Levenberg–Marquardt methods
cites work: Karush-Kuhn-Tucker systems: regularity conditions, error bounds and a class of Newton-type methods
cites work: Levenberg--Marquardt methods with strong local convergence properties for solving nonlinear equations with convex constraints
cites work: A method for the solution of certain non-linear problems in least squares
cites work: An Algorithm for Least-Squares Estimation of Nonlinear Parameters
cites work: Generalized equations and their solutions, part II: Applications to nonlinear programming
cites work: Q3881473
cites work: Q2765625
cites work: On the convergence properties of the Levenberg–Marquardt method
DOI: 10.1007/S10107-011-0486-7
description: scientific article; zbMATH DE number 6145967