On the Newton method for set-valued maps

DOI10.1016/j.na.2011.04.005zbMath1236.49068OpenAlexW2040542157MaRDI QIDQ654063

Juan-Miguel Gracia

Publication date: 21 December 2011

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/1822/14845

zbMATH Keywords

set-valued mapsNewton's methodvariational analysis

Mathematics Subject Classification ID

Nonlinear programming (90C30) Newton-type methods (49M15) Set-valued and variational analysis (49J53) Numerical methods for variational inequalities and related problems (65K15)

Related Items (11)

Solving ill-posed bilevel programs ⋮ Complexity of the Newton method for set-valued maps ⋮ Stability of metric regularity with set-valued perturbations and application to Newton's method for solving generalized equations ⋮ A Newton iteration for differentiable set-valued maps ⋮ Globally convergent coderivative-based generalized Newton methods in nonsmooth optimization ⋮ On the SCD semismooth* Newton method for generalized equations with application to a class of static contact problems with Coulomb friction ⋮ Closed relative trajectories for formation flying with single-input control ⋮ A general iterative procedure to solve generalized equations with differentiable multifunction ⋮ On (local) analysis of multifunctions via subspaces contained in graphs of generalized derivatives ⋮ Generalized Newton Algorithms for Tilt-Stable Minimizers in Nonsmooth Optimization ⋮ On a Semismooth* Newton Method for Solving Generalized Equations

Cites Work

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• Generalized Newton's method based on graphical derivatives
• Newton's method for generalized equations: a sequential implicit function theorem
• Local convergence of Newton's method for subanalytic variational inclusions
• Newton and other continuation methods for multivalued inclusions
• Newton's method for the solution of systems of equalities and inequalities
• A Continuous Dynamical Newton-Like Approach to Solving Monotone Inclusions
• Stability of inclusions: characterizations via suitable Lipschitz functions and algorithms
• On the convergence of some methods for variational inclusions
• On a Newton Type Iterative Method for Solving Inclusions

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