addGenConstrPWL: boundaries

Answered

Eva Bauer

June 07, 2023 13:59

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Hello,

I have a question concerning the PWL constraint. What does Gurobi do, if one of the variables (x and y in the constraint) would need to take a higher value than the defined intervals in the PWL constraints in order to comply with another constraint?

I'm looking at x = temperature and y = "coefiicient of performance" COP values of heat pumps.

I state, that the temperature has to be higher than another variable z. But it can happen, that in order to fullfill x >= z, x would have to take a value outside the intervals.

What will Gurobi do? Is it always infeasible in this case or does it just assign x to the highest possible value of the interval?

https://www.gurobi.com/documentation/9.5/refman/objectives.html#subsubsection:PiecewiseObj Here it says that values outside the bound are extrapolated with the gradient between the last two pairs. After this I think, that Gurobi will just extrapolate the values, am I right?

Thanks for your answer in advance!

Related to

• Piecewise Linear

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  Maliheh Aramon

  • Gurobi Staff

  June 07, 2023 22:07

  Hi Eva, 

   Yes, you are right. As described in the documentation, 

  The first pair and last pair of points each define a ray, so values outside the specified \(x\) values are extrapolated from these points.

  Of course, the LB and UB defined on the variable \(x\) would be respected. 

  Best regards,

  Maliheh

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