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A variant of Newton’s method for generalized equations
Palabras clave:
Set-valued mapping, Generalized equation, Linear convergence, Aubin continuity, 2000 Mathematics Subject Classification, Primary: 49J53, 47H04, Secondary: 65K10 (en)Descargas
Abstract. In this article, we study a variant of Newton’s method of the following form
0 ϵ ƒ(χk) + ɦ ∇ ƒ(χk) (χk+1 - χk) + F (χk+1),
where ƒ is a function whose Frechet derivative is K-lipschitz, F is a set-valued map between two Banach spaces X and Y and h is a constant. We prove that this method is locally convergent to x* a solution of
0 ϵ ƒ(χ) + F(χ),
if the set-valued map [ƒ(χ*) + ɦ ∇ ƒ(χ*) (. — x*) + F (.)]1 is Aubin continuous at (0, x*) and we also prove the stability of this method.
Referencias
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