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Quasi-Newton gradient method with analytical determination of the direction and length of step. (English) Zbl 0662.65053

The author presents a quasi-Newton method for determining the minimum of a function f: \(R^ n\to R\) continuously differentiable. One gives an algorithm for generating an approximating sequence of the Hessian matrix. Each element of this approximating sequence has the property that the product with the gradient determines not only the step-direction but also the step-length.
Reviewer: D.I.Duca

MSC:

65K05 Numerical mathematical programming methods
90C30 Nonlinear programming
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References:

[1] M. Aoki: Introduction to Optimization Techniques – Fundamentals and Applications of Nonlinear Programming. Macmillan, New York 1971. Russian translation: Nauka, Moscow 1977. · Zbl 0243.90031
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[4] B. T. Polyak: Vvedenie v optimizaciju. Nauka, Moscow 1983.
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