Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Proceedings of the American Mathematical Society
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 15A39, 90C05

Retrieve articles in all journals with MSC: 15A39, 90C05

Additional Information

PII: S 0002-9939(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

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia