FindMinimum convergence criteria

[Ray Koopman]

FindMinimum has four convergence tests, controlled by two parameters:
AccuracyGoal and PrecisionGoal.

The documentation says:

* The settings for AccuracyGoal and PrecisionGoal specify the number
of digits to seek in both the value of the position of the minimum,
and the value of the function at the minimum.

* FindMinimum continues until either of the goals specified by
AccuracyGoal or PrecisionGoal is achieved.

The second statement is clear: FindMinimum will quit if either
accuracy or precision is adequate. But does the first statement mean
that both the position and the function must be sufficiently accurate/
precise, or does it mean only that both are examined but either one
will suffice?

In other words, is the convergence criterion

((position is accurate) AND (function is accurate)) OR
((position is precise ) AND (function is precise )),

or is it

((position is accurate) OR (function is accurate)) OR
((position is precise ) OR (function is precise ))?

Setting one of AccuracyGoal or PrecisionGoal to Infinity will make
that goal unattainable, forcing the iterations to continue until the
other goal is reached. Is there any way to similarly ignore the error
in one of the position of the minimum or the value of the function,
so that the iterations will continue until the error in the other is
small enough?