  We study Landau-Zener transitions in a dissipative environment by means of
the numerically exact quasiadiabatic propagator path-integral. It allows to
cover the full range of the involved parameters. We discover a nonmonotonic
dependence of the transition probability on the sweep velocity which is
explained in terms of a simple phenomenological model. This feature, not
captured by perturbative approaches, results from a nontrivial competition
between relaxation and the external sweep.
