Getting non trivial solution from homogeneous system of equation

回答済み

Regina Charisty Kurnia

2020年06月30日 07:34

• 
• 
• 

Hello,

 

I am solving a MILP problem. However, one of the constraints requires a homogeneous system of linear equation.

 

 

for H is a non-invertible matrix, q and x are vectors (lists), M is sufficiently large and epsilon is sufficiently small.

 

I already wrote the codes in Python as below:

 

And I got this result:

 

I could get the result for x, but I want to avoid the trivial solution for q. Both variables are dependent to each other, so although the trivial solution is natural, there are still more options to get other values for q. Is there anyway to go around the constraints to get non-trivial solution?

 

Thank you.

0

• 正式なコメント

  

  Simranjit Kaur

  • Gurobi Staff

  2025年06月23日 03:10 編集済み

  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?.
• 

  Eli Towle

  • Gurobi Staff

  2020年07月01日 00:28 編集済み

  Hi Regina,

  By default, variables added using Model.addVars() are nonnegative. Perhaps this is the problem, since the solution to the system \( Hq = 0 \) is restricted to the set \( \{ q \colon q \geq 0 \} \). You can remove the lower bound on the \( q \) variables by adding \( \texttt{lb=-GRB.INFINITY} \) as a keyword argument to Model.addVars(). Could you try this?

  Also, note that you can use \( \texttt{x.sum()} \) to generate the objective function \( \sum_{i \in E} x_i \). This is a bit more concise. See tupledict.sum() for more information about this method.

  Thanks,

  Eli

  0
• 

  Regina Charisty Kurnia

  2020年07月01日 08:48

  • 
  • 
  • 

  Hi Eli,

   

  I tried your solution and it works just as I expected. Thank you very much!

   

   

  Kind regards,

  Regina

  0

投稿コメントは受け付けていません。