A semilocal convergence of a secant-type method for solving generalized equations

DOI10.1007/s11117-006-0044-3zbMath1118.47052OpenAlexW2007533038MaRDI QIDQ865017

Alain Piétrus, Saïd Hilout

Publication date: 13 February 2007

Published in: Positivity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11117-006-0044-3

zbMATH Keywords

iterative methodBanach spacesuperlinear convergencesemilocal convergence theoremmetric regularitydivided differenceset-valued mapAubin continuitycalmness properties

Mathematics Subject Classification ID

Set-valued and variational analysis (49J53) Iterative procedures involving nonlinear operators (47J25) Set-valued operators (47H04) Numerical solutions to equations with nonlinear operators (65J15)

Related Items (7)

Convergence analysis of the Gauss-Newton-type method for Lipschitz-like mappings ⋮ Secant-inexact projection algorithms for solving a new class of constrained mixed generalized equations problems ⋮ A Fréchet derivative-free cubically convergent method for set-valued maps ⋮ Local convergence of Newton's method for subanalytic variational inclusions ⋮ Convergence analysis of a family of Steffensen-type methods for generalized equations ⋮ On the convergence of extended Newton-type method for solving variational inclusions ⋮ An improved local convergence analysis for a two-step Steffensen-type method

Cites Work

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• Local convergence of some iterative methods for generalized equations.
• Semilocal convergence of the secant method under mild convergence conditions of differentiability
• Lipschitz Behavior of Solutions to Convex Minimization Problems
• Lipschitzian properties of multifunctions
• Complete Characterization of Openness, Metric Regularity, and Lipschitzian Properties of Multifunctions
• An Inverse Mapping Theorem for Set-Valued Maps
• Stability Theory for Parametric Generalized Equations and Variational Inequalities Via Nonsmooth Analysis
• Variational Analysis
• Set-valued analysis

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