  Optimal control theory implementations for an efficient population transfer
and creation of a maximum coherence in three-level system are considered. We
demonstrate that the half-STIRAP (stimulated Raman adiabatic passage) scheme
for creation of the maximum Raman coherence is the optimal solution according
to the optimal control theory. We also present a comparative study of several
implementations of optimal control theory applied to the complete population
transfer and creation of the maximum coherence. Performance of the conjugate
gradient method, the Zhu-Rabitz method and the Krotov method has been analyzed.
