Published

2006-01-01

An improved convergence analysis of a superquadratic method for solving generalized equations

Keywords:

Superquadratic convergence, Generalized equations, Radius of convergence, Aubin continuity, Pseudo-Lipschitz map, 2000 Mathematics Subject Classification, Primary: 65K10, 65G99, Secondary: 47H04, 49M15 (en)

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Authors

  • Cameron University, USA

Abstract. We provide a finer local convergence analysis than before [6]-[9] of a certain superquadratic method for solving generalized equations under Hölder continuity conditions.

Nosotros hacemos un análisis de convergencia local más fino que el proporcionado antes de [6]-[9] de cierto método supercuadrático para resolver ecuaciones generalizadas bajo ciertas condiciones de continuidad de Hölder.

References

I. K. Argyros, A unifying local-sem ilocal convergence analysis and applications for two-point Newton-like m ethods in Banach space, J. Math. Anal. Applic. 298 (2004), 374-397.

I. K. Argyros, Approximate Solution of Operator Equations with Applications, World Scientific Publ. Comp., New Jersey, USA, 2005.

I. K. Argyros, On the secant method for solving nonsmooth equations, J. Math. Anal. Applic. (to appear, 2006).

I. K. Argyros, D. Chen, & M. Tabatabai, The Halley-Werner method in Banach spaces, Revue d’Analyse Numerique et de theorie de l’Approximation, 1 (1994), 1-14.

J. P. Aubin, Lipschitz behavior of solutions to convex minimization problems, Math. Oper. Res. 9 (1984), 87-111.

J. P. Aubin & H. Frankowska, Set Valued Analysis, Birkhauser, Boston, 1990.

A. L. Dontchev, Local convergence of the Newton method for generalized equations, C.R.A.S. Paris 332 Ser. I (1996), 327-331.

A. L. Dontchev & W. W. Hager, An inverse function theorem for set-valued maps, Proc. Amer. Math. Soc. 121 (1994), 481-489.

M. H. Geoffroy & A. A. Pietrus, Superquadratic method for solving generalized equations in the Holder case, Ricerche di Matematica L II fasc. 2 (2003), 231-240.

A. D. Ioffe & V. M. Tikhomirov, Theory of Extremal Problems, North Holland, Amsterdam, 1979.

S. M. Robinson, Strong regular generalized equations, Math. Oper. Res. 5 (1980), 43-62.

How to Cite

APA

Ioannis K. (2006). An improved convergence analysis of a superquadratic method for solving generalized equations. Revista Colombiana de Matemáticas, 40(1), 65–73. https://revistas.unal.edu.co/index.php/recolma/article/view/94673

ACM

[1]
Ioannis K. 2006. An improved convergence analysis of a superquadratic method for solving generalized equations. Revista Colombiana de Matemáticas. 40, 1 (Jan. 2006), 65–73.

ACS

(1)
Ioannis K. An improved convergence analysis of a superquadratic method for solving generalized equations. rev.colomb.mat 2006, 40, 65-73.

ABNT

IOANNIS K. An improved convergence analysis of a superquadratic method for solving generalized equations. Revista Colombiana de Matemáticas, [S. l.], v. 40, n. 1, p. 65–73, 2006. Disponível em: https://revistas.unal.edu.co/index.php/recolma/article/view/94673. Acesso em: 9 mar. 2025.

Chicago

Ioannis K. 2006. “An improved convergence analysis of a superquadratic method for solving generalized equations”. Revista Colombiana De Matemáticas 40 (1):65-73. https://revistas.unal.edu.co/index.php/recolma/article/view/94673.

Harvard

Ioannis K. (2006) “An improved convergence analysis of a superquadratic method for solving generalized equations”, Revista Colombiana de Matemáticas, 40(1), pp. 65–73. Available at: https://revistas.unal.edu.co/index.php/recolma/article/view/94673 (Accessed: 9 March 2025).

IEEE

[1]
Ioannis K., “An improved convergence analysis of a superquadratic method for solving generalized equations”, rev.colomb.mat, vol. 40, no. 1, pp. 65–73, Jan. 2006.

MLA

Ioannis K. “An improved convergence analysis of a superquadratic method for solving generalized equations”. Revista Colombiana de Matemáticas, vol. 40, no. 1, Jan. 2006, pp. 65-73, https://revistas.unal.edu.co/index.php/recolma/article/view/94673.

Turabian

Ioannis K. “An improved convergence analysis of a superquadratic method for solving generalized equations”. Revista Colombiana de Matemáticas 40, no. 1 (January 1, 2006): 65–73. Accessed March 9, 2025. https://revistas.unal.edu.co/index.php/recolma/article/view/94673.

Vancouver

1.
Ioannis K. An improved convergence analysis of a superquadratic method for solving generalized equations. rev.colomb.mat [Internet]. 2006 Jan. 1 [cited 2025 Mar. 9];40(1):65-73. Available from: https://revistas.unal.edu.co/index.php/recolma/article/view/94673

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