[Ipopt] Optimality guarantees for convex problems?

Lasse Kliemann lasse-list-ipopt-2009 at mail.plastictree.net
Sat Oct 31 08:37:07 EDT 2009


I have questions concerning the behavior of Ipopt on convex
problems. The documentation reads:

   It is important to keep in mind that the algorithm is only 
   trying to find a local minimizer of the problem; if the 
   problem is nonconvex, many stationary points with different 
   objective function values might exist, and it depends on the 
   starting point and algorithmic choices which particular one 
   the method converges to.

Now, assume I have a problem expressed with smooth functions 
(say, polynomials) and an objective function that is convex on 
all R^n. Can I expect Ipopt to deliver a globally optimal 
solution then (probably up to small inaccuracies)?

If so, my second question concerns the case when the objective 
function is not convex on R^n, but at least the set K of feasible 
points is convex and the objective function is convex on K. Can I 
expect Ipopt to deliver a globally optimal solution ("globally" 
meaning: on K) then (probably up to small inaccuracies)?

The latter occurs frequently in my application, so it would be 
interesting to know.

By the way, thank you for your work on Ipopt!

Kind regards
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