How can this trial LP be infeasible?

Answered

Peter Shi

• January 23, 2021 10:22

Here is a trivial LP:

Minimize multi-objectives
 OBJ0: Priority=3 Weight=1 AbsTol=0 RelTol=0
 GOAL
Subject To
 GOAL = -10

------------------------------

Multi-objectives: solved in 0.02 seconds
Model is infeasible

 

But when I change -10 to 10, it becomes feasible. What's wrong with Gurobi?

0

• 

  Thomas Opfer

  • January 23, 2021 19:10

  

  

  I guess the problem is that lower bounds of variables are 0 if not specified otherwise.

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• 

  Peter Shi

  • January 25, 2021 21:11

  

  

  

  Thank you! You are right about the source of the problem. To fix the problem, I first added

  Bounds

  GOAL <= 0

  But it won't work. So I added

  -1000000000000000 <= GOAL <= 100000000000000

  It works! My suggestion is to always add, by default, a large range for every variable, even if the variable is already given a fixed value.

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• 

  Thomas Opfer

  • January 25, 2021 21:26

  

  

  Something like

  -inf <= GOAL <= inf

  should be the correct way to do this.

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• 

  Matthias Miltenberger

  Gurobi Staff

  • January 26, 2021 12:48

  Hi Peter,

  Thomas is absolutely right about the bounds. You should never use huge bounds to express unboundedness. This is almost guaranteed to cause numerical issues sooner or later.

  Please review our Guide on Numerics and this section on recommended ranges in particular.

  Please also note that the use of nonnegative variables is a standard convention in the mathematical programming community.

  Cheers,
  Matthias

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