Modeling square root of squared variable

Answered

DR

February 27, 2023 16:26

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Dear community,

I try to model the following objective function in Python:

x is the only variable, a and b are parameters.

I tried the following but it is not working properly:

x = m.addVars(i_max, j_max, vtype=GRB.CONTINUOUS, name='x')

# use z as auxiliary variable for (a+b*x)
z = m.addVars(k_max, 1, vtype=GRB.CONTINUOUS, name='z')

for k in range(0, k_max):
        z[k,0] = gp.quicksum(
            (a['a'][i,j,k] + b['b'][j,k] * x[i,j])
            for j in range(0, j_max)
            for i in range(0, i_max)
        )

z2 = m.addVar(vtype=GRB.CONTINUOUS, name='z2')
z2 = gp.quicksum( z[k,0] * z[k,0] for k in range(0, k_max) )

z3 = m.addVar(vtype=GRB.CONTINUOUS, name='z3')
c = m.addGenConstrLogA(z2, z3, 0.5, "c")

obj = gp.quicksum(
       (z[k,0] / z3)
       for k in range(0, k_max)
    )

model.setObjective(obj, GRB.MINIMIZE)
model.optimize()

Thanks for your help!

Related to

• Python
• Nonlinear

0

• 

  Riley Clement

  • Gurobi Staff

  February 28, 2023 00:18

  Hi DR,

  I cannot reproduce the exact issue you might be seeing because there are several definitions in your code which are not provided, e.g. i_max, j_max, k_max, a, b, etc

  However I can see an error where you are using z2 as an argument in

  c = m.addGenConstrLogA(z2, z3, 0.5, "c")

  Both the first two arguments need to be Gurobi variables.  You initially define z2 to be a Gurobi variable but then you overwrite on the next line, resulting in it being an expression.  You are probably wanting to do the following instead.

  z2 = m.addVar(vtype=GRB.CONTINUOUS, name='z2')
  m.addConstr(z2 == gp.quicksum( z[k,0] * z[k,0] for k in range(0, k_max) )

  - Riley

  1
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  DR

  February 28, 2023 07:15

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  Thanks a lot, Riley! 

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