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[Help-glpk] Deleting active constraints

From: Sylvain Fournier
Subject: [Help-glpk] Deleting active constraints
Date: Tue, 4 May 2010 18:01:01 -0300

Hi all!

I am quoting an almost three year-old-e-mail of this list about the deletion of active constraints in a LP, keeping the current basis in order not to solve the model from scratch. I used this method in my algorithm (removing the constraint bounds: GLP_FR), but I don't understand a point: when I solve the LP again, the first solution (at iteration 0) has a lower objective (all right) but the value of the infeasibility increases. How is it possible that the infeasibility increases although I removed a constraint?
I am (still) using the GLPK version 4.38.
Best regards,

Sylvain Fournier

If you delete some active row, i.e. the row, whose auxiliary variable
is non-basic, the number of rows is decreased by one while the number
of variables marked as basic remains the same, and the basis becomes
invalid. Similarly, if you delete some basic structural variable, the
number of rows remains the same while the number of basic variables
is decreased by one, so the basis again becomes invalid.

If a row is active, deleting it invalidates the basis as was explained
above. However, you can attain the same effect by *freeing* the row,
i.e. by changing its bounds to -inf and +inf, resp., in which case the
basis remains valid. Analogously, if a column is basic, you can change
both its bounds to 0, i.e. *fix* the structural variable at zero, rather
than delete it, in which case the basis again remains valid.

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