Consistency of linear inequalities over sets

Author:
Abraham Berman

Journal:
Proc. Amer. Math. Soc. **36** (1972), 13-17

MSC:
Primary 15A39; Secondary 90C05

DOI:
https://doi.org/10.1090/S0002-9939-1972-0309967-6

MathSciNet review:
0309967

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Abstract | References | Similar Articles | Additional Information

Abstract: Necessary and sufficient conditions for the equivalence of the statements: (I) The system , is consistent. (II) , are given in terms of the sets *S* and *T* and the matrix *A*. Sufficient conditions for this equivalence are obtained in the case where *S* and *T* are closed convex cones.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1972-0309967-6

Keywords:
Affine set,
closed convex cone,
consistency,
linear inequality,
linear transformation,
pointed cone,
polar,
polyhedral cone,
relative interior

Article copyright:
© Copyright 1972
American Mathematical Society