[Coin-ipopt] Limit on MU

Carl Damon Laird claird at andrew.cmu.edu
Wed Aug 3 11:49:23 EDT 2005

Hi Ivan,

I assume that the reason you want a smaller mu is to produce a solution 
that is tighter to the bound for the active variables.

It has been my experience that reducing dinfmaxtol (to something like 
1e-10) pulls things in tighter, although I have never done this with a 
large overall tolerance. Furthermore, I assume that you use a large 
tolerance because of noise in the problem (derivatives?) and this is not 
the case with my problems.

Anyway, it is something to try before modifying the code.



On Wed, 3 Aug 2005, Andreas Waechter wrote:

> Hi Ivan,
>> We've been exploring IPOPT (Fortran version) for some time in solving
>> our nonlinear programming problem and ran into a curious behavior.
> Out of curiosity:  What kind of problems are you solving?
>> We're in the unfortunate position of having to set DTOL rather large and
>> we've noticed that the barrier parameter is hard-bounded by DTOL/10.  In
>> your paper, you explain: "the update (7) does not allow the rule to
>> become smaller than necessary given the desired tolerance
>> \epsilon_{tol}, thus avoiding numerical difficulties at the end of the
>> optimization procedure."  We are unclear on what the specific numerical
>> difficulties would be for this primal-dual formulation of the problem.
>> Are there any results that have shown what the 'necessary' value of MU
>> should be in relation to the overall tolerance?
> If you would choose MU to be on the order of, say, 1e-16, you might run
> into problems because your slacks and bound multiplier values become very
> small (on the order of machine precision).  Therefore, the idea was that
> the mimimal value of the barrier parameter should be tied to the specified
> error tolerance.
> If you specify that you only want to solve the problem to a tolerance of,
> say, 1e-3, the lower bound on MU will be small enough so that your desired
> tolerance can be met, but not much smaller.  If you want to have the
> algorithm use a smaller value of MU (and therefore solve the
> complementarity condition more tightly than the other optimality
> conditions), you can change line 96 of update_mu.f accordingly.
>> Since I have you attention I can't resist asking if there are any
>> updates on when the C++ alpha version will be released?
> We hope to be ready to release the C++ version in about three weeks.
> Therefore, we are not making any more changes to the Fortran version
> (except for bug fixes).  The new version will not have all the "features"
> of the Fortran version (e.g., there will be no reduced-space option - and
> the limitied-memory quasi-Newton options for the full space will be added
> a little bit later).
> Hope this helps,
> Andreas
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