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authorDavid A. Madore <david+git@madore.org>2022-03-09 14:34:21 +0100
committerDavid A. Madore <david+git@madore.org>2022-03-09 14:34:21 +0100
commite683b39e0b5f8f8226514ed28ebc1547339e9d5c (patch)
tree3879319264337bb615c1bc6bb8c6f27458ca68db
parent62446ff800447eb1f75340f67f44e7cbf92e7a91 (diff)
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Typo/thinko in definition of dual to linear programming problem.HEADmaster
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@@ -1947,7 +1947,7 @@ devient de maximiser $v_+ - v_-$ sous les contraintes
\[-\sum_{a\in A_1} x_a \leq -1\]
\[(\forall b\in A_2)\;v_+ - v_- - \sum_{a \in A_1} u(a,b)\, x_a \leq 0\]
Le problème dual (minimiser ${^{\mathrm{t}}\textbf{q}} y$ sous les
-contraintes ${^{\mathrm{t}}\textbf{M}} y \geq {^\mathrm{t}\textbf{q}}$
+contraintes ${^{\mathrm{t}}\textbf{M}} y \geq {^\mathrm{t}\textbf{p}}$
et $y\geq 0$) est alors de minimiser $w_+ - w_-$ sous les contraintes
\[w_+\geq 0,\; w_- \geq 0,\;\; (\forall b\in A_2)\;y_b \geq 0\]
\[\sum_{b\in A_2} y_b \geq 1\]