Combining Different Types if Variables in Matrix Constraints

Ongoing

Satender .

December 25, 2021 12:43

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If I have the constraint of the form x_i  <= z_i , (i = 1,2, ..., n), where x_i are continuous and belong to interval [0,1], and  z_i's are binary. Both z_i's and x_i's are also present separately in various other constraints. 

Then, how do I add variables x_i and z_i separately to my model and use both in a single Constraint in matrix form (e.x.   A @ x , where x = [x_i z_i], a combination of both variables). 

One way is to construct matrix constraints using all the variables as x but, then I won't be able to use different types of vars.

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• Official comment

  

  Simranjit Kaur

  • Gurobi Staff

  June 23, 2025 02:42 Edited

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• 

  Mario Ruthmair

  • Gurobi Staff

  December 28, 2021 11:02

  Hi Mr. Satender,

  You could create a one-dimensional binary matrix variable including both variable sets x and z, and then change the type of the x variables to CONTINUOUS afterwards, as demonstrated below on a small example:

  A = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
  b = np.array([1, 2, 3])
  
  m = gp.Model("model")
  x = m.addMVar(3, vtype=GRB.BINARY, name="x")
  x[0].VType = GRB.CONTINUOUS
  
  m.addConstr(A @ x <= b, name="matrix")

  Best regards,
  Mario

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