Further insight into the Shamanskii modification of Newton method. (English) Zbl 1103.65071

Summary: A new Wolfe-type line search is proposed, and the global and superlinear convergence of Shamanskii’s method [cf. V. E. Shamanskij, On a modification of Newton’s method. Ukr. Mat. Zh. 19, 133–138 (1967; Zbl 0176.13802)] with the new line search are proved under mild assumptions. Furthermore, the iterative scheme of the Shamanskii method is also generalized.


65K05 Numerical mathematical programming methods
90C30 Nonlinear programming


Zbl 0176.13802


Full Text: DOI


[1] Shamanskii, V. E., On a modification of Newton’s method, Ukrainskyi Matematychnyi Zhurnal, 19, 133-138 (1967), (in Russian) · Zbl 0176.13802
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