| Title:
|
Two minimax-type methods for solving systems of nonlinear equations (English) |
| Author:
|
Hrouda, Jaroslav |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
14 |
| Issue:
|
1 |
| Year:
|
1969 |
| Pages:
|
29-53 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
The system of equations $h_i(x)=0\ (i=1,\ldots,r;\ x\in E_n)$ is solved by means of iterative methods of minimization of the functions A) $max_i\ h_i(x)$ under the conditions $h_i(x)\geq 0$, B) $max_i\ \left|h_i(x)\right|$. These methods are derived from the Zoutendijk's method of feasible directions. A good deal of attention is paid to their numerical aspects. (English) |
| Keyword:
|
operations research |
| MSC:
|
65.50 |
| idZBL:
|
Zbl 0167.18301 |
| idMR:
|
MR0235719 |
| DOI:
|
10.21136/AM.1969.103206 |
| . |
| Date available:
|
2008-05-20T17:44:15Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103206 |
| . |
| Reference:
|
[1] Zoutendijk G.: Methods of feasible directions;.Elsevier, Amsterdam 1960. Zbl 0097.35408 |
| Reference:
|
[2] Altman M.: A feasible direction method for solving the non-linear programming problem;.Bull. Acad. Polon. Sci., math., astr., phys. 12 (1964), No 1, 43-50. Zbl 0127.36705, MR 0165665 |
| Reference:
|
[3] Зуховицкий С. И., Поляк Р. А., Примак M. E.: Алгорифм для решения задачи выпуклого чебышевского приближения;.ДАН СССР 151 (1963), № 1, 27-30. Zbl 1145.93303 |
| Reference:
|
[4] Altman M.: Stationary points in non-linear programming;.Bull. Acad. Polon. Sci., math., astr., phys. 12 (1964), No 1, 29-35. Zbl 0123.37302, MR 0164810 |
| Reference:
|
[5] Hrouda J.: On a classification of stationary points in nonlinear programming;.this issue. Zbl 0167.18302 |
| Reference:
|
[6] Hadley G.: Nonlinear and dynamic programming;.Addison-Wesley, Reading 1964. Zbl 0179.24601, MR 0173543 |
| Reference:
|
[7] Зуховицкий С. И., Авдеева Л. И.: Линейное и выпуклое программирование;.Наука, Москва 1964. Zbl 1117.65300 |
| Reference:
|
[8] Юдин Д. Б., Гольштейн E. Г.: Линейное программирование;.Физматгиз, Москва 1963. Zbl 1145.93303 |
| Reference:
|
[9] Kelley J. E.: The cutting-plane method for solving convex programs;.J. SIAM 8 (1960), No 4, 703-712. MR 0118538 |
| Reference:
|
[10] Загускин В. Л.: Справочник по численным методам решения алгебраических и трансцендентных уравнений;.Физматгиз, Москва 1960. Zbl 1004.90500 |
| Reference:
|
[11] Фаддеев Д. К., Фаддеева В. H.: Вычислительные методы линейной алгебры;.Физматгиз, Москва 1963. Zbl 1145.93303 |
| Reference:
|
[12] Goldstein A. A.: Cauchy's method of minimization;.Numer. Math. 4 (1962), No 2, 146- 150. Zbl 0105.10201, MR 0141222, 10.1007/BF01386306 |
| Reference:
|
[13] Яковлев M. H.: О некоторых методах решения нелинейных уравнений;.Труды матем. инст. В. А. Стеклова 84, Наука, Москва 1965, 8-40. Zbl 1099.01519 |
| Reference:
|
[14] Hrouda J.: Řešení soustav nelineárních rovnic;.Závěrečná zpráva o úkolu R7.3/66, VÚTECHP, Praha 1966, 6-15. |
| . |
