Publicado

2000-07-01

Does Newton's method for set-valued maps converges uniformly in mild differentiability context?

Palabras clave:

Set-valued maps, Aubin continuity, generalized equations, Newton's method, superlinear uniform convergence (es)

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Autores/as

  • Alain Pietrus Université de Poitiers

In this article, we study the existence of Newton-type sequence for solving the equation y ϵ f(𝓍) + F(𝓍) where y is a small parameter, f is a function whose Fréchet derivative satisfies a Holder condition of the form II∇f(𝓍k) -∇f(x2)∥ ≤ K ∥lx1 - x2d and F is a set-valued map between two Banach spaces X and Y. We prove that the Newton-type method y ∈ f(𝓍k) +∇f(𝓍k)(𝓍k+1 - 𝓍k ) +F(𝓍k+1), is locally convergent to a solution of  y ϵ f(𝓍) + F(𝓍) if the set valued map (f(x* )+ ∇f(x* )(∙-𝓍*)+F(∙))-1 is Aubin continuous at (0,𝓍*) where 𝓍* is a solution of 0 ϵ f(𝓍) + F(𝓍). Moreover, we show that this convergence is superlinear uniformly in the parameter y and quadratic when d = 1.

Cómo citar

APA

Pietrus, A. (2000). Does Newton’s method for set-valued maps converges uniformly in mild differentiability context?. Revista Colombiana de Matemáticas, 34(2), 49–56. Recuperado a partir de https://revistas.unal.edu.co/index.php/recolma/article/view/33770

ACM

[1]
Pietrus, A. 2000. Does Newton’s method for set-valued maps converges uniformly in mild differentiability context?. Revista Colombiana de Matemáticas. 34, 2 (jul. 2000), 49–56.

ACS

(1)
Pietrus, A. Does Newton’s method for set-valued maps converges uniformly in mild differentiability context?. rev.colomb.mat 2000, 34, 49-56.

ABNT

PIETRUS, A. Does Newton’s method for set-valued maps converges uniformly in mild differentiability context?. Revista Colombiana de Matemáticas, [S. l.], v. 34, n. 2, p. 49–56, 2000. Disponível em: https://revistas.unal.edu.co/index.php/recolma/article/view/33770. Acesso em: 19 may. 2022.

Chicago

Pietrus, Alain. 2000. «Does Newton’s method for set-valued maps converges uniformly in mild differentiability context?». Revista Colombiana De Matemáticas 34 (2):49-56. https://revistas.unal.edu.co/index.php/recolma/article/view/33770.

Harvard

Pietrus, A. (2000) «Does Newton’s method for set-valued maps converges uniformly in mild differentiability context?», Revista Colombiana de Matemáticas, 34(2), pp. 49–56. Disponible en: https://revistas.unal.edu.co/index.php/recolma/article/view/33770 (Accedido: 19mayo2022).

IEEE

[1]
A. Pietrus, «Does Newton’s method for set-valued maps converges uniformly in mild differentiability context?», rev.colomb.mat, vol. 34, n.º 2, pp. 49–56, jul. 2000.

MLA

Pietrus, A. «Does Newton’s method for set-valued maps converges uniformly in mild differentiability context?». Revista Colombiana de Matemáticas, vol. 34, n.º 2, julio de 2000, pp. 49-56, https://revistas.unal.edu.co/index.php/recolma/article/view/33770.

Turabian

Pietrus, Alain. «Does Newton’s method for set-valued maps converges uniformly in mild differentiability context?». Revista Colombiana de Matemáticas 34, no. 2 (julio 1, 2000): 49–56. Accedido mayo 19, 2022. https://revistas.unal.edu.co/index.php/recolma/article/view/33770.

Vancouver

1.
Pietrus A. Does Newton’s method for set-valued maps converges uniformly in mild differentiability context?. rev.colomb.mat [Internet]. 1 de julio de 2000 [citado 19 de mayo de 2022];34(2):49-56. Disponible en: https://revistas.unal.edu.co/index.php/recolma/article/view/33770

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