Behavior of Newton-type methods near critical solutions of nonlinear equations with semismooth derivatives
DOI10.1007/s10957-023-02350-wMaRDI QIDQ6655783
Andreas Fischer, M. Jelitte, A. F. Izmajlov
Publication date: 27 December 2024
Published in: Journal of Optimization Theory and Applications (Search for Journal in Brave)
nonlinear equationextrapolation2-regularitynonlinear complementarity problemsingular solutionperturbed Newton methodconstrained equationcritical solutionacceptance of the full stepstrongly semismooth derivative
Newton-type methods (49M15) Nonsmooth analysis (49J52) Methods of quasi-Newton type (90C53) Numerical solutions to equations with nonlinear operators (65J15) Numerical methods for variational inequalities and related problems (65K15)
Cites Work
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- An LP-Newton method: nonsmooth equations, KKT systems, and nonisolated solutions
- On regularity conditions for complementarity problems
- Stabilized SQP revisited
- Levenberg--Marquardt methods with strong local convergence properties for solving nonlinear equations with convex constraints
- A Levenberg-Marquardt algorithm for unconstrained multicriteria optimization
- 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
- A simply constrained optimization reformulation of KKT systems arising from variational inequalities
- Stabilized sequential quadratic programming
- Local behavior of an iterative framework for generalized equations with nonisolated solutions
- Stability of possibly nonisolated solutions of constrained equations, with applications to complementarity and equilibrium problems
- 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
- A unified local convergence analysis of inexact constrained Levenberg-Marquardt methods
- On the quadratic convergence of the Levenberg-Marquardt method without nonsingularity assumption
- Inexact Levenberg-Marquardt method for nonlinear equations
- Stabilized sequential quadratic programming for optimization and a stabilized Newton-type method for variational problems
- Unit stepsize for the Newton method close to critical solutions
- Accelerating convergence of the globalized Newton method to critical solutions of nonlinear equations
- Newton-type methods near critical solutions of piecewise smooth nonlinear equations
- A nonsmooth version of Newton's method
- A family of Newton methods for nonsmooth constrained systems with nonisolated solutions
- Critical solutions of nonlinear equations: stability issues
- A globally convergent LP-Newton method
- THE LEVEL SET OF A SMOOTH MAPPING IN A NEIGHBORHOOD OF A SINGULAR POINT, AND ZEROS OF A QUADRATIC MAPPING
- Weak Sharp Minima in Mathematical Programming
- On the inexactness level of robust Levenberg–Marquardt methods
- Optimization and nonsmooth analysis
- On Solving Nonlinear Equations with Simple Singularities or Nearly Singular Solutions
- An Algorithm for Least-Squares Estimation of Nonlinear Parameters
- Equivalence of the Complementarity Problem to a System of Nonlinear Equations
- On the convergence properties of the Levenberg–Marquardt method
- Convergence Properties of the Inexact Levenberg-Marquardt Method under Local Error Bound Conditions
- Newton-Type Methods for Optimization and Variational Problems
- On Matrices Whose Real Linear Combinations are Nonsingular
- The Theory of 2-Regularity for Mappings with Lipschitzian Derivatives and its Applications to Optimality Conditions
- A method for the solution of certain non-linear problems in least squares
- Error bounds for 2-regular mappings with Lipschitzian derivatives and their applications
- Convergence conditions for Newton-type methods applied to complementarity systems with nonisolated solutions
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