Piecewise linear approximation to sigmoid function

Answered

JAMMAL Mahdi

• May 02, 2020 20:24

I am new to Gurobi, I'm trying to solve a problem with the following function as objective function: log(1+exp(-x)).  I know that I should use piecewise linear approximation to solve the problem. 

How can I do it using matlab? 

Regards

 

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• Official comment

  

  Simranjit Kaur

  Gurobi Staff

  • December 06, 2024 00:46

  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 why not try our AI Gurobot?.
• 

  Richard Oberdieck

  Gurobi Staff

  • May 04, 2020 11:23

  Hi Jammal,

   

  you can solve your problem by using functional constraints that were introduced in v9 of Gurobi. In Python, this can look as follows:

  m = gp.Model()
  
  # Add the first part
  x = m.addVar(lb=-np.inf)
  xNegative = m.addVar(lb=-np.inf)
  m.addConstr(xNegative == -x)
  
  # Now add the exponential
  y = m.addVar(lb=-np.inf)
  m.addGenConstrExp(xNegative, y)
  
  # Now the expression
  z = m.addVar()
  m.addConstr(z == 1+y)
  
  # The logarithm general constraint
  q = m.addVar(lb=-np.inf)
  m.addGenConstrLog(z, q, options="FuncPieces=-1 FuncPieceError=0.001") # This setting will make the approximation more exact

  This functionality is also available in the MATLAB API.

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