Getting the Right Minimum with Limits.

If [MIGrad]MIGRAD converges normally to a point where no parameter is near one of its limits, then the existence of limits has probably not prevented Minuit from finding the right minimum. On the other hand, if one or more parameters is near its limit at the minimum, this may be because the true minimum is indeed at a limit, or it may be because the minimizer has become ``blocked'' at a limit. This may normally happen only if the parameter is so close to a limit (internal value at an odd multiple of $\pm \{\pi 2\}$ that Minuit prints a warning to this effect when it prints the parameter values.

The minimizer can become blocked at a limit, because at a limit the derivative seen by the minimizer $F\; /\; P$_int

is zero no matter what the real derivative $F\; /\; P$_ext is.

$\{FP$_int}={FP_ext}{P_extP_int}={FP_ext}= 0

For a stepping method (like [SIMplex]SIMPLEX) this seldom poses any problem, but a method based on derivatives ([MIGrad]MIGRAD) may become blocked at such a value. If this happens, it may be necessary to move the value of the parameter in question a significant distance from the limit (with [SET PARameter]SET PARam) and restart the minimization, perhaps with that parameter fixed temporarily. We are investigating ways to induce Minuit to extricate itself from such situations automatically, but it is not so obvious as it seems, and for the moment must sometimes be done by hand.