Unit stepsize for the Newton method close to critical solutions

DOI10.1007/s10107-020-01496-zzbMath1470.65102OpenAlexW3016203065MaRDI QIDQ2020619

Andreas Fischer, Alexey F. Izmailov, Mikhail V. Solodov

Publication date: 23 April 2021

Published in: Mathematical Programming. Series A. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10107-020-01496-z

zbMATH Keywords

nonlinear equationextrapolationNewton methodlinear convergencesingular solutionsuperlinear convergencelinesearchcritical solution

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10)

Related Items (3)

Newton-type methods near critical solutions of piecewise smooth nonlinear equations ⋮ Accelerating convergence of the globalized Newton method to critical solutions of nonlinear equations ⋮ Accelerating convergence of a globalized sequential quadratic programming method to critical Lagrange multipliers

Cites Work

• Unnamed Item
• Unnamed Item
• An LP-Newton method: nonsmooth equations, KKT systems, and nonisolated solutions
• Stabilized SQP revisited
• An accelerated Newton method for equations with semismooth jacobians and nonlinear complementarity problems
• Starlike domains of convergence for Newton's method at singularities
• Superlinear convergence of a stabilized SQP method to a degenerate solution
• Critical solutions of nonlinear equations: local attraction for Newton-type methods
• Local attractors of Newton-type methods for constrained equations and complementarity problems with nonisolated solutions
• On the quadratic convergence of the Levenberg-Marquardt method without nonsingularity assumption
• Stabilized sequential quadratic programming for optimization and a stabilized Newton-type method for variational problems
• A family of Newton methods for nonsmooth constrained systems with nonisolated solutions
• Critical solutions of nonlinear equations: stability issues
• On Solving Nonlinear Equations with Simple Singularities or Nearly Singular Solutions
• An Algorithm for Least-Squares Estimation of Nonlinear Parameters
• Newton-Type Methods for Optimization and Variational Problems
• A method for the solution of certain non-linear problems in least squares

This page was built for publication: Unit stepsize for the Newton method close to critical solutions