Correo Electrónico
DNINFOA - SIA
Bibliotecas
Convocatorias
Identidad U.N.
Publicado
Superquadratic convergence of a Hummel-Seebeck type method
Convergencia supercuadrática de un método tipo Hummel-Seebeck
Palabras clave:
Set-valued mappings, M-pseudo-Lipschitzness, superquadratic convergence, Holder-type condition (en)Aplicaciones conjunto-valoradas, pseudo-Lipschitz, convergencia supercuadrática, condición de tipo Holder (es)
Descargas
Abstract. The cubic convergence of a method inspired by a Hummel and Seebeck for solving variational inclusions, has been showed when the second order Fréchet derivative of some function / satisfies a Lipschitz condition. Here, we prove the superquadratic convergence of this method whenever this second order Fréchet derivative satisfies a Holder condition.
La convergencia cúbica de un método de Hummel y Seebeck para resolver inclusiones variacionales ha sido probado cuando la derivada de Fréchet de segundo orden de alguna función / satisface una condición de Lipschitz. Aquí probamos la convergencia supercuadrática de este método siempre que esta derivada de Fréchet de segundo orden satisfaga una condición de Holder.
Referencias
J. P. Aubin, Lipschitz behavior of solutions to convex minimization problems, Mathematics of Operations Research 9 (1984), 87-111.
J. P. Aubin and H. Frankowska, Set-valued analysis, Birkhâuser, Boston, 1990.
A. L. Dontchev and W. W. Hager, An inverse function theorem for set-valued maps, P roc. Amer. Math. Soc. 121 (1994), 481-489.
A. L. Dontchev, M. Quincampoix, and N. Zlateva, Aubin criterion for metric regularity, Journal of Convex Anal. 13 (2006), 281-297.
A. L. Dontchev and R. T. Rockafellar, Characterizations of strong regularity for variational inequalities over polyhedral convex sets, SIAM J. Optim. 6 (1996), no. 4, 1087-1105.
______ Regularity and conditioning of solutions mappings in variational analysis, Set-valued Anal. 12 (2004), 79-109.
M. H. Geoffroy, C. Jean-Alexis, and A. Pietrus, A Hummel-Seebeck type method for variational inclusions, Preprint.
M. H. Geoffroy and A. Pietrus, A superquadratic method for solving generalized equations in the Holder case, Ricerce di Matematica LII (2003), no. 1, 231-240.
P. M. Hummel and C. L. Seebeck Jr., A generalization of Taylor’s expansion, Amer. Math. Monthly 56 (1949), 243-247.
A. D. Ioffe and V. M. Tikhomirov, Theory of extremal problems, North Holland, Amsterdam, 1979.
C. Jean-Alexis, A cubic method without second order derivative for solving variational inclusions, C. R. A cad. Bulg. Sci. 59 (2006), no. 12, 1213-1218.
A. Pietrus, Generalized equations under mild differentiability conditions, Revista de la Real Academia de Ciencias Exactas de Madrid 94 (2000), no. 1, 15-18.
R. T. Rockafellar and R. Wets, Variational analysis, Comprehensive Studies in Mathematics, vol. 317, Springer, New York, 1998.
