Abstract
A minimization problem is considered for the case when the minimand function and the functions defining the set of equality and inequality constraints are known with an error. A regularized Steffensen's method for the solution of this problem is proposed. It is shown that, when the variation of the regularization and penalty parameters is compatible with the errors, the sequence generated by this method converges in norm to the minimum point with minimum norm.
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Literature Cited
A. N. Tikhonov and V. Ya. Arsenin,Methods of Solution of Ill-Posed Problems [in Russian], Nauka, Moscow (1979).
F. P. Vasil'ev,Methods of Solution of Extremal Problems [in Russian], Nauka, Moscow (1981).
S. Yu. Ul'm, "A generalization of Steffensen's method for solving nonlinear operator equations,"Zh. Vychisl. Mat. Mat. Fiz. 4, No. 6, 1093–1097 (1964).
Additional information
Translated from Metody Matematicheskogo Modelirovaniya, Avtomatizatsiya Obrabotki Nablyudenii i Ikh Primeneniya, pp. 15–23, 1986.
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Vasil'ev, F.P. Regularization of Steffensen's method with inexactly specified initial data. Comput Math Model 1, 162–168 (1990). https://doi.org/10.1007/BF01129059
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DOI: https://doi.org/10.1007/BF01129059