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.
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Clark, S. Necessary and Sufficient Conditions for Solving Infinite-Dimensional Linear Inequalities. Positivity 10, 475–489 (2006). https://doi.org/10.1007/s11117-005-0042-x
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DOI: https://doi.org/10.1007/s11117-005-0042-x