Modeling quadratic constraints in different variables

Answered

Surya Narayanan Hari

October 23, 2020 08:31

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I saw on the website that one can write quadratic constraints of the form x*x + y*y <= c, but Is it possible to write a constraint of the form x^T y <= c where x and y are vectors?

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• Official comment

  

  Simranjit Kaur

  • Gurobi Staff

  December 06, 2024 00:40

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• 

  Matthias Miltenberger

  • Gurobi Staff

  October 23, 2020 11:38 Edited

  Hi Surya,

  Yes, this is possible:

  import gurobipy as gp
  import numpy as np
  
  m = gp.Model()
  n = 3
  x = m.addMVar(n, name='x')
  y = m.addMVar(n, name='y')
  c = 2
  
  m.addConstr(x @ np.eye(3) @ y <= c)

  Resulting in this QP:

  Minimize
  
  Subject To
  qc0: [ x[0] * y[0] + x[1] * y[1] + x[2] * y[2] ] <= 2
  Bounds
  End

  Cheers,
  Matthias

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