Geodesic
Two minimax-type methods for solving systems of nonlinear equations
Applications of Mathematics, Tome 14 (1969) no. 1, pp. 29-53
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
DOI : 10.21136/AM.1969.103206
Classification : 65.50
Keywords: operations research 
@article{10_21136_AM_1969_103206,
     author = {Hrouda, Jaroslav},
     title = {Two minimax-type methods for solving systems of nonlinear equations},
     journal = {Applications of Mathematics},
     pages = {29--53},
     year = {1969},
     volume = {14},
     number = {1},
     doi = {10.21136/AM.1969.103206},
     mrnumber = {0235719},
     zbl = {0167.18301},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1969.103206/}
}
TY  - JOUR
AU  - Hrouda, Jaroslav
TI  - Two minimax-type methods for solving systems of nonlinear equations
JO  - Applications of Mathematics
PY  - 1969
SP  - 29
EP  - 53
VL  - 14
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.21136/AM.1969.103206/
DO  - 10.21136/AM.1969.103206
LA  - en
ID  - 10_21136_AM_1969_103206
ER  - 
%0 Journal Article
%A Hrouda, Jaroslav
%T Two minimax-type methods for solving systems of nonlinear equations
%J Applications of Mathematics
%D 1969
%P 29-53
%V 14
%N 1
%U http://geodesic.mathdoc.fr/articles/10.21136/AM.1969.103206/
%R 10.21136/AM.1969.103206
%G en
%F 10_21136_AM_1969_103206
Hrouda, Jaroslav. Two minimax-type methods for solving systems of nonlinear equations. Applications of Mathematics, Tome 14 (1969) no. 1, pp. 29-53. doi: 10.21136/AM.1969.103206

[1] Zoutendijk G.: Methods of feasible directions. Elsevier, Amsterdam 1960. | Zbl

[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. | MR | Zbl

[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

[4] Altman M.: Stationary points in non-linear programming. Bull. Acad. Polon. Sci., math., astr., phys. 12 (1964), No 1, 29-35. | MR | Zbl

[5] Hrouda J.: On a classification of stationary points in nonlinear programming. this issue. | Zbl

[6] Hadley G.: Nonlinear and dynamic programming. Addison-Wesley, Reading 1964. | MR | Zbl

[7] Зуховицкий С. И., Авдеева Л. И.: Линейное и выпуклое программирование. Наука, Москва 1964. | Zbl

[8] Юдин Д. Б., Гольштейн E. Г.: Линейное программирование. Физматгиз, Москва 1963. | Zbl

[9] Kelley J. E.: The cutting-plane method for solving convex programs. J. SIAM 8 (1960), No 4, 703-712. | MR

[10] Загускин В. Л.: Справочник по численным методам решения алгебраических и трансцендентных уравнений. Физматгиз, Москва 1960. | Zbl

[11] Фаддеев Д. К., Фаддеева В. H.: Вычислительные методы линейной алгебры. Физматгиз, Москва 1963. | Zbl

[12] Goldstein A. A.: Cauchy's method of minimization. Numer. Math. 4 (1962), No 2, 146- 150. | DOI | MR | Zbl

[13] Яковлев M. H.: О некоторых методах решения нелинейных уравнений. Труды матем. инст. В. А. Стеклова 84, Наука, Москва 1965, 8-40. | Zbl

[14] Hrouda J.: Řešení soustav nelineárních rovnic. Závěrečná zpráva o úkolu R7.3/66, VÚTECHP, Praha 1966, 6-15.

Cité par Sources :