  Adiabatic processes driven by non-Hermitian, time-dependent Hamiltonians may
be sped up by generalizing inverse engineering techniques based on Berry's
transitionless driving algorithm or on dynamical invariants. We work out the
basic theory and examples described by two-level Hamiltonians: the acceleration
of rapid adiabatic passage with a decaying excited level and of the dynamics of
a classical particle on an expanding harmonic oscillator.
