The determination of necessary and sufficient conditions for the existence of a solution to the 3 × 3 × 3 multi-index problem

Graham Smith; Jeremy Dawson

Aplikace matematiky (1979)

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

Abstract

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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.

How to cite

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Smith, 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

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  1. M. L. Balinski, An Algorithm for Finding all Vertices of Convex Polyhedral Sets, SIAM Jnl 9 (1961), 72-78. (1961) Zbl0108.33203MR0142057
  2. N. Maňas, J. Nedoma, Finding all Vertices of a Convex Polyhedron, Numerische Mathematik 72(1968), 226-229. (1968) Zbl0165.51801MR0235705
  3. T. H. Mattheis, 10.1287/opre.21.1.247, Opns. Res. 21 (1973), 247-260. (1973) MR0437087DOI10.1287/opre.21.1.247
  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. (1974) Zbl0284.90056MR0349219
  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. (1975) Zbl0323.90030MR0446492
  6. S. Vajda, Mathematical Programming, Addison-Wesley (1961). (1961) Zbl0102.36401MR0135621

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