# Two minimax-type methods for solving systems of nonlinear equations

Aplikace matematiky (1969)

• Volume: 14, Issue: 1, page 29-53
• ISSN: 0862-7940

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## Abstract

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The system of equations ${h}_{i}\left(x\right)=0\phantom{\rule{4pt}{0ex}}\left(i=1,...,r;\phantom{\rule{4pt}{0ex}}x\in {E}_{n}\right)$ is solved by means of iterative methods of minimization of the functions A) $ma{x}_{i}\phantom{\rule{4pt}{0ex}}{h}_{i}\left(x\right)$ under the conditions ${h}_{i}\left(x\right)\ge 0$, B) $ma{x}_{i}\phantom{\rule{4pt}{0ex}}\left|{h}_{i}\left(x\right)\right|$. These methods are derived from the Zoutendijk’s method of feasible directions. A good deal of attention is paid to their numerical aspects.

## How to cite

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Hrouda, Jaroslav. "Two minimax-type methods for solving systems of nonlinear equations." Aplikace matematiky 14.1 (1969): 29-53. <http://eudml.org/doc/14576>.

@article{Hrouda1969,
abstract = {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 $h_i(x)\ge 0$, 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.},
author = {Hrouda, Jaroslav},
journal = {Aplikace matematiky},
keywords = {operations research},
language = {eng},
number = {1},
pages = {29-53},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Two minimax-type methods for solving systems of nonlinear equations},
url = {http://eudml.org/doc/14576},
volume = {14},
year = {1969},
}

TY - JOUR
AU - Hrouda, Jaroslav
TI - Two minimax-type methods for solving systems of nonlinear equations
JO - Aplikace matematiky
PY - 1969
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 14
IS - 1
SP - 29
EP - 53
AB - 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 $h_i(x)\ge 0$, 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.
LA - eng
KW - operations research
UR - http://eudml.org/doc/14576
ER -

## References

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1. Zoutendijk G., Methods of feasible directions;, Elsevier, Amsterdam 1960. (1960) Zbl0097.35408
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. (1964) Zbl0127.36705MR0165665
3. Зуховицкий С. И., Поляк Р. А., Примак M. E., Алгорифм для решения задачи выпуклого чебышевского приближения;, ДАН СССР 151 (1963), № 1, 27-30. (1963) Zbl1145.93303
4. Altman M., Stationary points in non-linear programming;, Bull. Acad. Polon. Sci., math., astr., phys. 12 (1964), No 1, 29-35. (1964) Zbl0123.37302MR0164810
5. Hrouda J., On a classification of stationary points in nonlinear programming;, this issue. Zbl0167.18302
7. Зуховицкий С. И., Авдеева Л. И., Линейное и выпуклое программирование;, Наука, Москва 1964. (1964) Zbl1117.65300
8. Юдин Д. Б., Гольштейн E. Г., Линейное программирование;, Физматгиз, Москва 1963. (1963) Zbl1145.93303
9. Kelley J. E., The cutting-plane method for solving convex programs;, J. SIAM 8 (1960), No 4, 703-712. (1960) MR0118538
10. Загускин В. Л., Справочник по численным методам решения алгебраических и трансцендентных уравнений;, Физматгиз, Москва 1960. (1960) Zbl1004.90500
11. Фаддеев Д. К., Фаддеева В. H., Вычислительные методы линейной алгебры;, Физматгиз, Москва 1963. (1963) Zbl1145.93303
12. Goldstein A. A., 10.1007/BF01386306, Numer. Math. 4 (1962), No 2, 146- 150. (1962) Zbl0105.10201MR0141222DOI10.1007/BF01386306
13. Яковлев M. H., О некоторых методах решения нелинейных уравнений;, Труды матем. инст. В. А. Стеклова 84, Наука, Москва 1965, 8-40. (1965) Zbl1099.01519
14. Hrouda J., Řešení soustav nelineárních rovnic;, Závěrečná zpráva o úkolu R7.3/66, VÚTECHP, Praha 1966, 6-15. (1966)

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