degenerate solution

[Gary]

Hi,

I have a general question: does Gurobi be able to give some information about whether the solution is degenerate or whether the multiple shadow price exists.

I will be grateful if some people can provide some insight.

Thank you

[des...@gurobi.com]

Sorry, we don't have that ability.  You would have to figure this out by searching for multiple solutions.

Dr Amal de Silva
Gurobi Optimization

[Tobias Achterberg]

Well, I guess you are talking about LPs (and not MIPs). For those, the usual LP
theory applies: a solution is degenerate if it has basic elements that have a
solution value that is equal to one of the bounds.

On the primal side this means:
If a basic variable has a solution value x that is equal to the variable's lower
or upper bound, then the solution is degenerate.
If a basic row has a slack value of 0, then the solution is degenerate.

On the dual side this means:
If a non-basic variable has reduced costs of 0, then the solution is degenerate.
If a non-basic row has a dual solution value of 0, then the solution is degenerate.

And in practice this means: pretty much every solution is degenerate ;)


Regards,

Tobias