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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Consistency of linear inequalities over sets

Author: Abraham Berman
Journal: Proc. Amer. Math. Soc. 36 (1972), 13-17
MSC: Primary 15A39; Secondary 90C05
MathSciNet review: 0309967
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Abstract: Necessary and sufficient conditions for the equivalence of the statements: (I) The system $ b - Ax \in T,x \in S$, is consistent. (II) $ y \in {T^ \ast },{A^H}y \in {S^ \ast } \Rightarrow \operatorname{Re} (b,y) \geqq 0$, 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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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