How can I add constraints on the rank of the matrix

Answered

Shawn Xu

November 26, 2022 00:35

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X is a 20*20 square matrix, and I want to let the number of nonzero rows in X <= 10,  how can I write the constraint? Appreciate your help

Related to

• General Constraints
• Matrix API

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  Maliheh Aramon

  • Gurobi Staff

  November 26, 2022 01:53

  Hi Shawn, 

  Please see the code snippet below using the Gurobi Matrix API in version 10.0 as an example implementation. It is assumed that \(X\) is a binary matrix and a nonzero row refers to a row with at least one of its elements being equal to 1. 

  m = gp.Model("")
  
  X = m.addMVar((20, 20), vtype=GRB.BINARY, name="x")
  y = m.addMVar(20, vtype=GRB.BINARY, name="y")
  
  # Ensure at most 10 non-zero rows are selected
  m.addConstr(y.sum() <= 10)
  
  # If row i is not selected, all its elements equals 0
  m.addConstr(X.sum(axis=1) <= 20 * y, name="")
  # If row i is selected, at least one of its elements equals 1
  m.addConstr(X.sum(axis=1) >= y, name="")

   

  Best regards,

  Maliheh

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  Shawn Xu

  November 26, 2022 15:15

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  Thank you Maliheh! Solved!

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