Float exponent of a variable

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BISWAJIT KAR

2022年02月04日 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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• 正式なコメント

  

  Simranjit Kaur

  • Gurobi Staff

  2025年11月16日 23:44

  This post is more than three years old. Some information may not be up to date. For current information, please check the Gurobi Documentation or Knowledge Base. If you need more help, please create a new post in the community forum, or try Gurobot, our chatbot interface offering instant, expert-level support.
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  Zed Dean

  • Gurobi Staff

  2022年02月05日 14:06 編集済み

  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

  2022年02月07日 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

  2022年02月08日 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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