  The article considers a two-level open quantum system, whose evolution is
governed by the Gorini--Kossakowski--Lindblad--Sudarshan master equation with
Hamiltonian and dissipation superoperator depending, correspondingly, on
piecewise constant coherent and incoherent controls with constrained
magnitudes. Additional constraints on controls' variations are also considered.
The system is analyzed using Bloch parametrization of the system's density
matrix. We adapt the section method for obtaining outer parallelepipedal and
pointwise estimations of reachable and controllability sets in the Bloch ball
via solving a number of problems for optimizing coherent and incoherent
controls with respect to some objective criteria. The differential evolution
and dual annealing optimization methods are used. The numerical results show
how the reachable sets' estimations depend on distances between the system's
initial states and the Bloch ball's center point, final times, constraints on
controls' magnitudes and variations.
