Float exponent of a variable

Ongoing

BISWAJIT KAR

February 04, 2022 07:11

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if the objective function is 

x^0.2+y^0.4

the n how to solve such problems?

Do we still have to introduce auxiliary variable and constraint?

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  Zed Dean

  • Gurobi Staff

  February 05, 2022 14:06 Edited

  Hello Biswajit,

  I would try to introduce two  auxiliary variables:

  \begin{array}{l}
  a=x^{0.2} \\
  b=y^{0.4}
  \end{array}

  $$
  \text { min } a+b
  $$

  Then add the two constraints using Model.addGenConstrPow() (gurobi.com) as follow: 

  model.addGenConstrPow(x, a, 0.2)

  model.addGenConstrPow(y, b, 0.4)

  PWL  piecewise-linear constraints are an approximation, it affects the model's accuracy. Including a non-convex, piecewise linear may significantly increase the cost of solving the model. The Graph below illustrates the non-convex nature of your equation.

  

  Best Regards

  Zed

   

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  BISWAJIT KAR

  February 07, 2022 05:05

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  Dear Zed Dean, Thanks a lot for your response. The above question is just an example. I am solving similar questions.

  I am still getting a bit confused. So, is the following how the code is supposed to be written?

  import gurobipy as gp
  m.gp.Model('float')
  
  x=m.addVar(vtype=GRB.CONTINUOUS, name='x')
  y=m.addVar(vtype=GRB.CONTINUOUS, name='y')
  
  #Auxilary verb
  a=m.addVar(vtype=GRB.CONTINUOUS, name='a')
  b=m.addVar(vtype=GRB.CONTINUOUS, name='b')
  
  m.addGenConstrPow(x, a, 0.2)
  m.addGenConstrPow(y, b, 0.4)
  
  
  

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  Zed Dean

  • Gurobi Staff

  February 08, 2022 16:15

  Hello Biwajit,

  Seems correct so far, you need to add the objective and then you should be fine 

  Yours

  Zed

   

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