Geodesic
On maximizing a concave function subject to linear constraints by Newton's method
Applications of Mathematics, Tome 13 (1968) no. 4, pp. 339-355

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

MR Zbl
The paper deals with an adaptation of Newton's method for solving nonlinear programming problems. The adaptation is derived by replacing the gradient direction in Rosen's method by Newton's direction and both its convergence and practical aspects are discussed. Convergence properties of another adaptation of Newton's method (suggested by Hájek) are studied, too.
The paper deals with an adaptation of Newton's method for solving nonlinear programming problems. The adaptation is derived by replacing the gradient direction in Rosen's method by Newton's direction and both its convergence and practical aspects are discussed. Convergence properties of another adaptation of Newton's method (suggested by Hájek) are studied, too.
DOI : 10.21136/AM.1968.103178
Classification : 65K05, 90C26, 90C30 
Žáčková, Jitka. On maximizing a concave function subject to linear constraints by Newton's method. Applications of Mathematics, Tome 13 (1968) no. 4, pp. 339-355. doi: 10.21136/AM.1968.103178
@article{10_21136_AM_1968_103178,
     author = {\v{Z}\'a\v{c}kov\'a, Jitka},
     title = {On maximizing a concave function subject to linear constraints by {Newton's} method},
     journal = {Applications of Mathematics},
     pages = {339--355},
     year = {1968},
     volume = {13},
     number = {4},
     doi = {10.21136/AM.1968.103178},
     mrnumber = {0256732},
     zbl = {0212.18202},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1968.103178/}
}
TY  - JOUR
AU  - Žáčková, Jitka
TI  - On maximizing a concave function subject to linear constraints by Newton's method
JO  - Applications of Mathematics
PY  - 1968
SP  - 339
EP  - 355
VL  - 13
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.21136/AM.1968.103178/
DO  - 10.21136/AM.1968.103178
LA  - en
ID  - 10_21136_AM_1968_103178
ER  - 
%0 Journal Article
%A Žáčková, Jitka
%T On maximizing a concave function subject to linear constraints by Newton's method
%J Applications of Mathematics
%D 1968
%P 339-355
%V 13
%N 4
%U http://geodesic.mathdoc.fr/articles/10.21136/AM.1968.103178/
%R 10.21136/AM.1968.103178
%G en
%F 10_21136_AM_1968_103178

[1] J. Hájek: Minimalisace nákladů při dosažení předepsané přesnosti současně u několika odhadů. Apl. mat., 7 (1962), p. 405-425. | MR

[2] S. Karlin: Mathematical Methods and Theory in Games. Programming and Economics, Vol. I, London 1959. | MR

[3] J. B. Rosen: The Gradient Projection Method for Nonlinear Programming. Part I. Linear Constraints. J. Soc. Industr. Appl. Math., 8 (1960), p. 181 - 217. | DOI | MR

[4] J. Žáčkova: Dva příspěvky k matematickému programování. Kandidátská disertační práce, matematicko-fyzikální fakulta Karlovy university, Praha 1966.

Cité par Sources :