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Local analysis of a cubically convergent method for variational inclusions

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Burnet S., Pietrus A.

Applicationes Mathematicae

2011

tom 38

nr 2

183-191

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 $ℝ^q$ to the closed subsets of $ℝ^q$. 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 multipoint iteration method under center-Hölder continuity conditions

100%

Cabuzel C., Pietrus A.

Applicationes Mathematicae

2007

tom 34

nr 4

493-503

We prove the existence of a sequence $(x_k)$ satisfying $0 ∈ f(x_k) +∑_{i=1}^M a_i ∇ f(x_k+β_i(x_{k+1}-x_k))(x_{k+1}-x_k)+F(x_{k+1})$, 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.

Ograniczanie wyników

2 Applicationes Mathematicae

2 Pietrus A.

1 Burnet S.

1 Cabuzel C.

1 2011

1 2007

Wyniki wyszukiwania

Local analysis of a cubically convergent method for variational inclusions

Solving variational inclusions by a multipoint iteration method under center-Hölder continuity conditions