Local convergence of some iterative methods for generalized equations.

DOI10.1016/j.jmaa.2003.10.008zbMath1044.65044OpenAlexW1963863778MaRDI QIDQ1428240

Michel H. Geoffroy, Alain Piétrus

Publication date: 14 March 2004

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2003.10.008

zbMATH Keywords

set-valued mapsBanach spacesquadratic convergenceNewton methodnonlinear operator equationsecant methodsuper-linear convergencepseudo-Lipschitz continuityregula-falsi method

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Numerical solutions to equations with nonlinear operators (65J15)

Related Items (11)

Iterative solving of generalized equations with calm solution mappings ⋮ A semilocal convergence of a secant-type method for solving generalized equations ⋮ Convergence of inexact Newton methods for generalized equations ⋮ Secant-inexact projection algorithms for solving a new class of constrained mixed generalized equations problems ⋮ Extended Newton-type method for nonsmooth generalized equation under \((n, \alpha)\)-point-based approximation ⋮ Local convergence of Newton's method for subanalytic variational inclusions ⋮ Convergence analysis of a family of Steffensen-type methods for generalized equations ⋮ A general iterative procedure to solve generalized equations with differentiable multifunction ⋮ Local convergence of Newton-like methods for generalized equations ⋮ A general iterative procedure for solving nonsmooth generalized equations ⋮ Convergence analysis of a method for variational inclusions

Cites Work

• Finding zeros of analytic functions: \(\alpha\)-theory for secant type methods
• Lipschitz Behavior of Solutions to Convex Minimization Problems
• Lipschitzian properties of multifunctions
• Complexity of Bezout's Theorem I: Geometric Aspects
• Complete Characterization of Openness, Metric Regularity, and Lipschitzian Properties of Multifunctions
• An Inverse Mapping Theorem for Set-Valued Maps
• Variational Analysis
• Characterizations of Strong Regularity for Variational Inequalities over Polyhedral Convex Sets
• Set-valued analysis
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