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Wang, Chang-Yu; Chen, Yuan-Yuan; Du, Shou-Qiang

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

Appl. Math. Comput. 180, No. 1, 46-52 (2006).
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.

Cited in 9 Documents

MSC:

65K05 Numerical mathematical programming methods
90C30 Nonlinear programming

Keywords:

unconstrained optimization; Shamanskii method; global and superlinear convergence; line search; Newton’s method

Citations:

Zbl 0176.13802

Software:

KELLEY
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\textit{C.-Y. Wang} et al., Appl. Math. Comput. 180, No. 1, 46--52 (2006; Zbl 1103.65071)
Full Text: DOI

References:

[1] Shamanskii, V. E., On a modification of Newton’s method, Ukrainskyi Matematychnyi Zhurnal, 19, 133-138 (1967), (in Russian) · Zbl 0176.13802
[2] Gill, P. E.; Murray, W., Newton-type methods for unconstrained and linearly constrained optimization, Mathematical Programming, 7, 311-350 (1974) · Zbl 0297.90082
[3] Hammerlin, G.; Hoffmann, K. H., Numerische Mathematik (1989), Springer-Verlag: Springer-Verlag New York · Zbl 0669.65001
[4] Kelley, C. Y., Iterative Methods for Optimization (1999), SIAM: SIAM Philadelphia, PA · Zbl 0934.90082
[5] Ortega, J. M.; Rheinboldt, W. C., Iterative Solution of Nonlinear Equations in Several Variables (1970), Academic Press: Academic Press New York, NY · Zbl 0241.65046
[6] Bertsekas, D. P., Constrained Optimization and Lagrange Multiplier Methods (1980), Academic Press: Academic Press New York, NY
[7] Lamparillo, F.; Sciandrone, M., Global convergence technique for the Newton method with periodic Hessian evaluation, Journal of Optimization Theory and Applications, 111, 2, 341-358 (2001) · Zbl 1032.90045
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