Piece-wise Linear multi objective (Python-gurobi)
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Hello everybody,
So I am solving a LP model where I use the model.setPWLObj() function to maximize the sum of all the pwl approximations of my variables. (Actually, there is no variable that does not need a pwl approximation in my problem).
Now I want to introduce some auxiliary variables to the model (I want to add an additional variable to each of the existing ones) so that the original ones x_i are now x_i + x_i_new for all variables i.
In this way, I am trying to approximate with PWL approx. the new variables x_i + x_i_new (because the original non-linear functions that I am approximating remain the same, since I am just adding an additional amount to the actual values of the original variables).
Now, the function setPWLObj() only accepts Var objects and not LinExpr (since x_i + x_i_new turns out to be a LinExpr and not a variable anymore!).
Does anybody know any approach to tackle this problem?
Thank you very much!
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You can create a(nother) new variable, set it equal to \( x_i + x^{\textrm{new}}_i \), then set that variable's piecewise-linear objective term using Model.setPWLObj(). E.g.:
z = m.addVar(lb=-GRB.INFINITY, name='z')
m.addConstr(z == x + xnew, name='set_auxiliary_z')
m.setPWLObj(z, xpts, ypts)0 -
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