[Coin-ipopt] Restoration Phase Failed

[Andreas Waechter]

Hi Roy,

> Does any one have any idea about Restoration Phase Failed in IPOPT?

That's a difficult question :)

The algorithm implemented in Ipopt sometimes reverts to a "restoration 
phase", the task of which is to simply reduce the infeasibiliy.  This is 
done under certain conditions, which usually mean that the optimization 
might be "stuck" in some sense.

However, sometimes the restoration phase might run itself into problems. 
Or, it sometimes happens that Ipopt wants to call the restoration phase at 
a point that is already feasibly (i.e., the restoration phase cannot 
reduce the infeasibility anymore).  In those cases, Ipopt's exit message 
is "Restoration Phase Failed".

Now, the question you are really asking is what that means for the problem 
itself.  Well, theoretically, this should not happen if the problem 
statement satisfies certain conditions (see the Ipopt global convergence 
paper).  One of the assumptions is that the gradients of the active 
constraints are linearly independent, and this is a condition that could 
be violated in practice.  So, it might be that Ipopt is trying to solve a 
problem which does not satify a "constraint qualification" at the feasible 
point it is converging to.  (Note, if a constraint qualification does not 
hold at the optimal solution of the problem, then the KKT conditions 
cannot be satisfied at this point - since Ipopt is trying to find a point 
that satisfies the KKT conditions, it must run into trouble).  There might 
be some workaround for such a case, and Ipopt might stop with a message 
like "cannot find KKT point, constraint violation might be violated".

Other than that, the restoration phase can also fail if the problem is 
really nasty, if derivatives are incorrect, the problem is badly scaled...

I hope this helps at least a little bit...

Cheers

Andreas