Does Newton's method for set-valued maps converges uniformly in mild differentiability context?
A superquadratic method for solving variational inclusions under weak conditions.
Newton-secant Method for Functions With Values in a Cone
2010 Mathematics Subject Classification: 49J53, 47H04, 65K10, 14P15.
Solving variational inclusions by a multipoint iteration method under center-Hölder continuity conditions
We prove the existence of a sequence satisfying , where f is a function whose second order Fréchet derivative ∇²f satifies a center-Hölder condition and F is a set-valued map from a Banach space X to the subsets of a Banach space Y. We show that the convergence of this method is superquadratic.
Local analysis of a cubically convergent method for variational inclusions
This paper deals with variational inclusions of the form 0 ∈ φ(x) + F(x) where φ is a single-valued function admitting a second order Fréchet derivative and F is a set-valued map from to the closed subsets of . When a solution z̅ of the previous inclusion satisfies some semistability properties, we obtain local superquadratic or cubic convergent sequences.
Solving variational inclusions by a method obtained using a multipoint iteration formula.
A variant of Newton's method for generalized equations.
On the convergence of some methods for variational inclusions
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