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I keep seeing the term "optimal basis", but can't see an explicit definition anywhere. I suppose it means something like "the basis at an optimal solution"?

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    $\begingroup$ Yes, the set of non negative variables that give you an optimal solution. $\endgroup$ – Kuifje Oct 28 '19 at 20:18
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More precisely, it's a basis such that the corresponding basic solutions of the primal and dual problems are both feasible (and thus optimal). This excludes a degenerate basis in which the basic solution of the primal problem happens to be optimal but is not obviously so (because the basic solution of the dual problem is not feasible).

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