Abstract
The cutting-plane method of J.E. Kelley [3] is widely used in convex programming. There are some modifications of this method (see, e.g. [4]), which in some cases accelerate its convergence. In this paper we discuss another modification of the Kelley method based on the idea described in [2] for solving equation f (x) = 0 with multiple roots by the Newton method. It is well-known that if an initial approximation is close enough to the root (and some additional conditions are satisfied) then the Newton method is of quadratic rate of convergence. But it is not the case if, for example, f (x) = x2 where x ∈ El. Then the multiplicity of the root x* = 0 is m = 2.
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References
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© 1985 Springer-Verlag Berlin Heidelberg
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Tarasov, V.N., Popova, N.K. (1985). A Modification of the Cutting-Plane Method with Accelerated Convergence. In: Demyanov, V.F., Pallaschke, D. (eds) Nondifferentiable Optimization: Motivations and Applications. Lecture Notes in Economics and Mathematical Systems, vol 255. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-12603-5_26
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DOI: https://doi.org/10.1007/978-3-662-12603-5_26
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