arctan in gUrobi optimization (python)

Answered

CHAYMAE MAKRI

• November 21, 2022 09:54

Hello, 

how can I add this constraint?

for i in N:

    for e in M: 

           b[i][e]=arctan(P[i] - Pc[i][e] * x [i,e])

where x is the binary variable, Pc is the decision variable, and P is a constant.

error (TypeError: must be real number, not gurobipy.LinExpr)

Thanks

0

• 

  Jaromił Najman

  Gurobi Staff

  • November 21, 2022 13:14

  Hi Chaymae,

  Currently, the \(\arctan\) function is not supported in Gurobi. The only way to add your constraint would be to use an approximation of the \(\arctan\) function. You could use the addGenConstrPWL method to construct a piecewise-linear approximation.

  import gurobipy as gp
  from gurobipy import GRB
  import math
  
  def f(u):
    return math.atan(u)
  
  m = gp.Model()
  
  lbz = -2
  ubz =  2
  z = m.addVar(lb=lbz, ub=ubz, vtype=GRB.CONTINUOUS, name="z")
  y = m.addVar(lb=-math.pi/2, ub=math.pi/2, vtype=GRB.CONTINUOUS, name="y")
  
  # Compute piecewise-linear arctan function for z
  npts = 101
  ptu = []
  ptf = []
  for i in range(npts):
      ptu.append(lbz + (ubz - lbz) * i / (npts - 1))
      ptf.append(f(ptu[i]))
  
  # Add constraint y = arctan(z) as piecewise-linear approximation
  m.addGenConstrPWL(z,y,ptu,ptf,"PWLarctan")

  Best regards, 
  Jaromił

  0

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