×

Differential gradient methods. (English) Zbl 0405.65040


MSC:

65K10 Numerical optimization and variational techniques
65L05 Numerical methods for initial value problems involving ordinary differential equations
90C99 Mathematical programming
Full Text: DOI

References:

[1] Himmelblau, D. M., Applied Nonlinear Programming (1972), McGraw-Hill: McGraw-Hill New York · Zbl 0521.93057
[2] Ortega, J. M.; Reinboldt, W. C., Iterative Solution of Nonlinear Equations in Several Variables (1970), Academic Press: Academic Press New York/London · Zbl 0241.65046
[3] Davidon, W. C., Variable Metric Methods for Minimization, A.E.C. Research and Development Report No. ANL-5990 (Rev.) (1959) · Zbl 0204.49602
[4] Broyden, C. G., Quasi-Newton methods and their application to function minimization, Math. Comp., 21, 368 (1967) · Zbl 0155.46704
[5] Fletcher, R. R.; Powell, M. J.D, A rapidly convergent descent method for minimization, Comput. J., 6, 163 (1963) · Zbl 0132.11603
[6] Fletcher, R., A new approach to variable metric algorithms, Comput. J., 13, 317 (1970) · Zbl 0207.17402
[7] Varga, L., A class of methods for function minimization, Studia Sci. Math. Hungar., 4, 291 (1969) · Zbl 0187.12604
[8] Daniel, J. N., Convergent Step Sizes for Curvilinear Path Methods of Minimization, (CNA-29 (1971), Center for Numerical Analysis, University of Texas: Center for Numerical Analysis, University of Texas Austin)
[9] Botsaris, C. A.; Jacobson, D. H., A Newton-type curvilinear search method for optimization, J. Math. Anal. Appl., 54, 217-229 (1976) · Zbl 0331.49026
[10] Jacobson, D. H.; Oksman, D. H.; Oksman, W., An algorithm that minimizes homogeneous functions of \(N\) variables in \(N + 2\) iterations and rapidly minimizes general functions, J. Math. Anal. Appl., 38, 535 (1972) · Zbl 0202.16501
[11] Botsaris, C. A., Differential Descent Methods for Function Minimization, (Doctoral Thesis (August 1975), University of the Witwatersrand: University of the Witwatersrand Johannesburg, South Africa) · Zbl 0446.90079
[12] Polak, E., Computational Methods in Optimization: A Unified Approach (1971), Academic Press: Academic Press New York
[13] Davidenko, D. F., On a new method of numerical solution of systems of nonlinear equations, Dokl. Akad. Nauk. USSR (N.S.), 88, 601 (1953) · Zbl 0050.12103
[14] Botsaris, C. A.; Jacobson, D. H., Minimization of a nonlinear function in many variables; a differential equation approach, (Paper presented at a Symposium on Differential Equations held at The Council for Scientific and Industrial Research. Paper presented at a Symposium on Differential Equations held at The Council for Scientific and Industrial Research, Pretoria (April 1975)) · Zbl 0331.49026
[15] J. S. Kowalik and K. G. Ramakrishnan; J. S. Kowalik and K. G. Ramakrishnan · Zbl 0351.90052
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.