| Title:
|
The determination of necessary and sufficient conditions for the existence of a solution to the $3\times3\times3$ multi-index problem (English) |
| Author:
|
Smith, Graham |
| Author:
|
Dawson, Jeremy |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
24 |
| Issue:
|
3 |
| Year:
|
1979 |
| Pages:
|
201-208 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| Summary:
|
Modifications to a procedure for determining necessary and sufficient conditions for the existence of a solution to the multi-index problem are described. These modifications reduce the computation required to such an extent that necessary and sufficient conditions for the existence of a solution to the 3x3x3 multi-index problem can now be determined. These conditions are given in this paper. (English) |
| Keyword:
|
necessary and sufficient conditions |
| Keyword:
|
existence of a solution |
| Keyword:
|
3x3x3 multi-index problem |
| Keyword:
|
existence conditions |
| Keyword:
|
existence of feasible solutions |
| Keyword:
|
convex polyhedron |
| Keyword:
|
multi-index-problems |
| Keyword:
|
surrogate linear program |
| MSC:
|
90C05 |
| MSC:
|
90C08 |
| idZBL:
|
Zbl 0453.90061 |
| idMR:
|
MR0530908 |
| DOI:
|
10.21136/AM.1979.103797 |
| . |
| Date available:
|
2008-05-20T18:11:50Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103797 |
| . |
| Reference:
|
[1] M. L. Balinski: An Algorithm for Finding all Vertices of Convex Polyhedral Sets.SIAM Jnl 9 (1961), 72-78. Zbl 0108.33203, MR 0142057 |
| Reference:
|
[2] N. Maňas, J. Nedoma: Finding all Vertices of a Convex Polyhedron.Numerische Mathematik 72(1968), 226-229. MR 0235705 |
| Reference:
|
[3] T. H. Mattheis: An Algorithm for Determining Irrelevant Constraints and all Vertices in Systems of Linear Inequalities.Opns. Res. 21 (1973), 247-260. MR 0437087, 10.1287/opre.21.1.247 |
| Reference:
|
[4] G. Smith: A Procedure for Determining Necessary and Sufficient Conditions for the Existence of a Solution to the Multi-Index Problem.Aplikace Matematiky 19 (1974), 177-183. Zbl 0284.90056, MR 0349219 |
| Reference:
|
[5] G. Smith: On the Morávek and Vlach Conditions for the Existence of a Solution to the Multi-Index Problem.Aplikace Matematiky 20 (1975), 432-435. Zbl 0323.90030, MR 0446492 |
| Reference:
|
[6] S. Vajda: Mathematical Programming.Addison-Wesley (1961). Zbl 0102.36401, MR 0135621 |
| . |
