Hudzovič, Peter Quasi-Newton gradient method with analytical determination of the direction and length of step. (English) Zbl 0662.65053 Kybernetika 24, No. 5, 378-393 (1988). 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 Keywords:gradient method; determination of step-direction and step-length; quasi- Newton method PDFBibTeX XMLCite \textit{P. Hudzovič}, Kybernetika 24, No. 5, 378--393 (1988; Zbl 0662.65053) Full Text: EuDML Link 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 [2] P. E. Gill W. Murray, M. H. Wright: Practical Optimization. Academic Press, New York 1981. Russian translation: Mir, Moscow 1985. · Zbl 0503.90062 [3] M. Maňas: Optimization Methods. SNTL, Praha 1979. In Czech. [4] B. T. Polyak: Vvedenie v optimizaciju. Nauka, Moscow 1983. [5] G. V. Reklaitis A. Ravindran, K. M. Ragsdell: Engineering Optimization – Methods and Applications. J. Wiley and Sons, New York 1983. Russian translation: Mir, Moscow 1986. [6] A. G. Sukharev A. V. Timokhov, V. V. Fedorov: Kurs metodov optimizacii. Nauka, Moscow 1986. · Zbl 0602.90091 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.