| Title:
|
On maximizing a concave function subject to linear constraints by Newton's method (English) |
| Author:
|
Žáčková, Jitka |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
13 |
| Issue:
|
4 |
| Year:
|
1968 |
| Pages:
|
339-355 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. () |
| MSC:
|
65K05 |
| MSC:
|
90C26 |
| MSC:
|
90C30 |
| idZBL:
|
Zbl 0212.18202 |
| idMR:
|
MR0256732 |
| DOI:
|
10.21136/AM.1968.103178 |
| . |
| Date available:
|
2008-05-20T17:43:00Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103178 |
| . |
| Reference:
|
[1] J. Hájek: Minimalisace nákladů při dosažení předepsané přesnosti současně u několika odhadů.Apl. mat., 7 (1962), p. 405-425. MR 0155383 |
| Reference:
|
[2] S. Karlin: Mathematical Methods and Theory in Games.Programming and Economics, Vol. I, London 1959. MR 1160778 |
| Reference:
|
[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. MR 0112750, 10.1137/0108011 |
| Reference:
|
[4] J. Žáčkova: Dva příspěvky k matematickému programování.Kandidátská disertační práce, matematicko-fyzikální fakulta Karlovy university, Praha 1966. |
| . |
