  The classical Ka\v{c}anov scheme for the solution of nonlinear variational
problems can be interpreted as a fixed point iteration method that updates a
given approximation by solving a linear problem in each step. Based on this
observation, we introduce a modified Ka\v{c}anov method, which allows for
(adaptive) damping, and, thereby, to derive a new convergence analysis under
more general assumptions and for a wider range of applications. For instance,
in the specific context of quasilinear diffusion models, our new approach does
no longer require a standard monotonicity condition on the nonlinear diffusion
coefficient to hold. Moreover, we propose two different adaptive strategies for
the practical selection of the damping parameters involved.
