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[RFC] Translate empty column rule and reduction to apply! syntax

Open mtanneau opened this issue 5 years ago • 0 comments

This is mostly straightforward.

One open question: how should we handle unbounded columns with close-to-zero objective? For instance: if a problem has an empty column with no lower bound and objective coeff of 1e-30, should we declare it dual infeasible?

Since empty columns are just empty rows in the dual, I would suggest to follow the same idea: we use a dual feasibility tolerance ϵ_d, and declare dual infeasibility if column j is empty, has no lower (resp. upper) bound and its objective is greater (resp. smaller) than ϵ_d (resp. -ϵ_d).

Obviously, using a "dual feasibility" tolerance for MIPs could raise some eyebrows.

mtanneau avatar Jan 31 '21 16:01 mtanneau