Adding a constraint on the norm

Answered

Nicolas Schlegel

October 20, 2023 09:17

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Hello, 

I would like to add the following constraint :

Where :

- s is a size 2U vector

- beta is a size 1 variable 

- A_r is a size 2Ux2B matrix

- l_0 is a float

- U is a size 2B x l variable

- L is size l float vector

- eta is a float

So only U and beta are variables.

 

I modeled U and beta as MVars. I used the following code snippet to add the constraint :

norm = gp.norm(s_r - beta*a_r@(l_0 + u @ l_array), 2)
m.addConstr(norm <= eta)

However, running this code leads to the following error message :

'<=' not supported between instances of 'GenExprNorm' and 'float'

I did not find a solution form the other questions related to this error message. Thank you in advance for the help !

 

Related to

• General Constraints
• Error

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  Matthias Miltenberger

  • Gurobi Staff

  October 20, 2023 09:59

  Hi Nicolas,

  You need to introduce an auxiliary variable that takes the value of the norm and construct the constraint using that new variable:

  norm = gp.norm(s_r - beta*a_r@(l_0 + u @ l_array), 2)
  aux_norm = m.addVar(ub=eta, name="norm")
  m.addConstr(norm == aux_norm)

  That should do the trick.

  Cheers,
  Matthias

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  Nicolas Schlegel

  October 20, 2023 11:37

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  Thank you for the quick answer.

  I changed the constraint with the code snipped you gave. However, I now receive the following error (model here refers to a class from another library) : 

  m.addConstr(mse_norm == aux_norm)
    File "src\gurobipy\genexpr.pxi", line 24, in gurobipy.GenExpr.__eq__
  RuntimeError: Exception encountered when calling layer 'model' (type Model) 
  10003

  From my understanding, 10003 is a gurobi error code, however, there is no error message along with this error code.

   

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  Eli Towle

  • Gurobi Staff

  October 20, 2023 21:18 Edited

  Try introducing auxiliary variables equal to \(\texttt{s_r - beta * a_r @ (l_0 + u @ l_array)}\). Then, introduce one additional auxiliary variable equal to the L2 norm of those variables. For example:

  aux = m.addMVar(shape=(2 * U,), lb=-GRB.INFINITY, name="aux")
  aux_norm = m.addMVar(shape=(1,), name="aux_norm")
  
  m.addConstr(aux == s_r - beta * a_r @ (l_0 + u @ l_array), name="set_aux")
  m.addConstr(aux_norm == gp.norm(aux, 2), name="set_aux_norm")
  m.addConstr(aux_norm <= eta, name="norm_ub")

  Alternatively, you could model your norm constraint without the use of gurobipy's norm() function:

  aux = m.addMVar(shape=(2 * U,), lb=-GRB.INFINITY, name="aux")
  
  m.addConstr(aux == s_r - beta * a_r @ (l_0 + u @ l_array), name="set_aux")
  m.addConstr(aux @ aux <= eta**2, "norm_ub")

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