Consistency of linear inequalities over sets

Berman, Abraham

doi:10.1090/S0002-9939-1972-0309967-6

Consistency of linear inequalities over sets
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by Abraham Berman PDF

Proc. Amer. Math. Soc. 36 (1972), 13-17 Request permission

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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A note on Farkas lemmas over cone domains