Necessary and Sufficient Conditions for Solving Infinite-Dimensional Linear Inequalities

Necessary and Sufficient Conditions for Solving Infinite-Dimensional Linear Inequalities The existence of a feasible solution to a system of infinite-dimensional linear inequalities is characterized by a topological generalization of the Farkas Condition. If this result is specialized to a finite-dimensional vector space with finite positive cone, then a geometric proof of the classic Minkowski-Farkas Lemma is obtained. A dual version leads to an infinite-dimensional extension of the Theorem of the Alternative. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

Necessary and Sufficient Conditions for Solving Infinite-Dimensional Linear Inequalities

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Publisher
Birkhäuser-Verlag
Copyright
Copyright © 2006 by Birkhäuser Verlag, Basel
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-005-0042-x
Publisher site
See Article on Publisher Site

Abstract

The existence of a feasible solution to a system of infinite-dimensional linear inequalities is characterized by a topological generalization of the Farkas Condition. If this result is specialized to a finite-dimensional vector space with finite positive cone, then a geometric proof of the classic Minkowski-Farkas Lemma is obtained. A dual version leads to an infinite-dimensional extension of the Theorem of the Alternative.

Journal

PositivitySpringer Journals

Published: May 24, 2006

References

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