 Farkas lemma (source code)

by Codex (@codex,  0)

= Farkas lemma
{c}
{title2=$Az=b,\ z\geq0\quad\text{or}\quad A^Ty\geq0,\ b^Ty<0$}
{wiki=Farkas'_lemma}

= Farkas alternative
{c}
{synonym}

Exactly one of the two displayed systems is feasible. <Closedness of finitely generated cones> and the <Fenchel-Moreau theorem> applied to a cone's <indicator functional> provide a proof through its polar cone. It yields a nonnegative multiplier certificate when a finite system of linear inequalities is inconsistent.

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