[Cbc] Strictly positive costs in minimization problem?

[Jakob Helbrink]

Hello,

I am working with a relatively large minimization problem where the number
of variables are 100.000-200.000. Since the computational time gets reduced
significantly without integer variables(approx. 1/3 of the variables were
initially integers) I am trying to formulate this without using integer
variables.

In order to formulate the LP without integers I have introduced another
variable *c*. The variables are linked mathematically as:

*(a-b) = c*, *where (a, b) are both continuous variables(in theory -inf<
(a, b) < inf.)  *

However, in the objective function the cost of *c *is *strictly* positive,
meaning that the cost(penalty) should not be able to take negative
values. In other words, I would like to "cap" the cost to be strictly
positive or equal to zero.
What I would like to achieve would be to disregard this cost in the solver
if its negative.
Any ideas?

Hopefully I managed to describe the problem in an graspable way, if not let
me know and I'll give it another try.

Regards,
Jakob
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