logistics function

Answered

El W

• August 26, 2023 14:17

I am solving an optimization problem in C++ with 

Min L(z); 

such that L(y_si<w,x_si>) = log(1+exp(L(z)) .

In this case is it necessary to create new grbvar ywx and ywx and addconstr (model.addQVar( z2== L(z)), and model.addGenConstrExp(z2, z2_exp) for the exp(L(z) part? and similar logic for the log(1+z2_exp) part? or any other way to deal with the log and exp. 

Related to

• General Constraints

0

• 

  Jaromił Najman

  Gurobi Staff

  • August 28, 2023 07:20
  • Edited

  Currently, the way you describe is the only way to model that kind of nonconvex function in Gurobi, i.e., you have to model

  \[\begin{align*}
  w_1 &= L(z)\\
  w_2 &= \exp(w_1)\\
  w_3 &= 1 + w_2\\
  w_4 &= \log(w_3)
  \end{align*}\]

  where \(w_i\) are auxiliary variables and the functions \(\exp, \log\) are implemented via the general constraints feature. Note that it is of high importance to provide tight variable bounds for variable \(w_1\) because it is the argument variable for the \(\exp\) function which already for very small input values achieves huge output. For \(w_3\), it is important to make sure that it is not too close to \(0\) to avoid the very steep part of \(\log\).

  Your title states "logistic function". Note that Gurobi has a general constraint describing the logistic function. However, it is different from the one you use but maybe you can still make use of it.

  Best regards, 
  Jaromił

  0

Please sign in to leave a comment.