# The determination of necessary and sufficient conditions for the existence of a solution to the $3\times 3\times 3$ multi-index problem

Aplikace matematiky (1979)

- Volume: 24, Issue: 3, page 201-208
- ISSN: 0862-7940

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topSmith, Graham, and Dawson, Jeremy. "The determination of necessary and sufficient conditions for the existence of a solution to the $3\times 3\times 3$ multi-index problem." Aplikace matematiky 24.3 (1979): 201-208. <http://eudml.org/doc/15095>.

@article{Smith1979,

abstract = {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.},

author = {Smith, Graham, Dawson, Jeremy},

journal = {Aplikace matematiky},

keywords = {necessary and sufficient conditions; existence of a solution; 3x3x3 multi-index problem; existence conditions; existence of feasible solutions; convex polyhedron; multi-index-problems; surrogate linear program; necessary and sufficient conditions; existence of a solution; 3x3x3 multi-index problem; existence conditions; existence of feasible solutions; convex polyhedron; multi-index-problems; surrogate linear program},

language = {eng},

number = {3},

pages = {201-208},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {The determination of necessary and sufficient conditions for the existence of a solution to the $3\times 3\times 3$ multi-index problem},

url = {http://eudml.org/doc/15095},

volume = {24},

year = {1979},

}

TY - JOUR

AU - Smith, Graham

AU - Dawson, Jeremy

TI - The determination of necessary and sufficient conditions for the existence of a solution to the $3\times 3\times 3$ multi-index problem

JO - Aplikace matematiky

PY - 1979

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 24

IS - 3

SP - 201

EP - 208

AB - 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.

LA - eng

KW - necessary and sufficient conditions; existence of a solution; 3x3x3 multi-index problem; existence conditions; existence of feasible solutions; convex polyhedron; multi-index-problems; surrogate linear program; necessary and sufficient conditions; existence of a solution; 3x3x3 multi-index problem; existence conditions; existence of feasible solutions; convex polyhedron; multi-index-problems; surrogate linear program

UR - http://eudml.org/doc/15095

ER -

## References

top- M. L. Balinski, An Algorithm for Finding all Vertices of Convex Polyhedral Sets, SIAM Jnl 9 (1961), 72-78. (1961) Zbl0108.33203MR0142057
- N. Maňas, J. Nedoma, Finding all Vertices of a Convex Polyhedron, Numerische Mathematik 72(1968), 226-229. (1968) MR0235705
- T. H. Mattheis, 10.1287/opre.21.1.247, Opns. Res. 21 (1973), 247-260. (1973) MR0437087DOI10.1287/opre.21.1.247
- 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. (1974) Zbl0284.90056MR0349219
- 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. (1975) Zbl0323.90030MR0446492
- S. Vajda, Mathematical Programming, Addison-Wesley (1961). (1961) Zbl0102.36401MR0135621

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