Hello,<div><br></div><div>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. </div>
<div><br></div><div>In order to formulate the LP without integers I have introduced another variable <b>c</b>. The variables are linked mathematically as:</div><div><br></div><div><b>(a-b) = c</b>, <i>where (a, b) are both continuous variables(in theory -inf< (a, b) < inf.) </i></div>
<div><br></div><div>However, in the objective function the cost of <i><b>c </b></i>is <i>strictly</i> 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. </div>
<div>What I would like to achieve would be to disregard this cost in the solver if its negative. </div><div>Any ideas?</div><div><br></div><div>Hopefully I managed to describe the problem in an graspable way, if not let me know and I'll give it another try. </div>
<div><br></div><div>Regards,</div><div>Jakob</div><div><br></div>