Optimization
The function to be optimized has the form:
R=Σ|Icalc-Iexp|/ΣIexp*100%, where
Icalc is the total
calculated scattering intensity for all planes giving contribution into a
some peak of the experimental diffraction pattern,
Iexp is the integral
intensity of this peak. This kind of function is less subjected by influence
of errors in integral intensities than traditional function
R=Σ(Icalc-Iexp)2/ΣIexp2*100%.
For optimization the well-known "downhill simplex" algorithm is used. This algorithm is one from
most efficient algorithms of local optimization. Of course, in the case of
multi-extremal function this kind of algorithms can find the "global" extreme
only accidentally. However, the numerous experiments showed that in moving from
various initial magnetic structures the algorithm converges approximately to one
and the same structure. Apparently, it is possible to deduce the conclusion that,
although the optimizing function is multi-extremal, the local minima form
insignificant "roughnesses" on the "slopes" of the global minima. It should be
noted that no algorithm of global optimization can guarantee the finding of the
single global minimum.
