[RFC] Translate empty column rule and reduction to apply! syntax #18
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mtanneau
commented
Jan 31, 2021
| @@ -458,7 +458,7 @@ function presolve!(ps::PresolveData{T}) where {T} | |||
| @_return_if_inferred remove_dominated_columns!(ps) | |||
| end | |||
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| @_return_if_inferred remove_empty_columns!(ps) | |||
| @_return_if_inferred apply!(ps, RemoveEmptyColumns(), config) # Why this here?? | |||
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I have no idea why this was here in the first place
joehuchette
approved these changes
Feb 1, 2021
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| ## Presolve | ||
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| If column $j$ is empty, variable $x_{j}$ is fixed to $x_{j}^{*}$ as follows |
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Nit:
Suggested change
| If column $j$ is empty, variable $x_{j}$ is fixed to $x_{j}^{*}$ as follows | |
| If column $j$ is empty, variable $x_{j}$ is fixed to $x_{j}^{*}$ as follows: |
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| If column $j$ is empty, variable $x_{j}$ is fixed to $x_{j}^{*}$ as follows | ||
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| | $c_{j}$ | $l_{j}$ | $u_{j}$ | $x^{*}_{j}$ | |
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This is all assuming minimization, correct?
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Correct. I'll mention it in the docs.
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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 columnjis empty, has no lower (resp. upper) bound and its objective is greater (resp. smaller) thanϵ_d(resp.-ϵ_d).Obviously, using a "dual feasibility" tolerance for MIPs could raise some eyebrows.