[Coin-ipopt] Limit on MU

[Andreas Waechter]

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