  We consider the convergence of iterative solvers for problems of nonlinear
magnetostatics. Using the equivalence to an underlying minimization problem, we
can establish global linear convergence of a large class of methods, including
the damped Newton-method, fixed-point iteration, and the Kacanov iteration,
which can all be interpreted as generalized gradient descent methods. Armijo
backtracking isconsidered for an adaptive choice of the stepsize. The general
assumptions required for our analysis cover inhomogeneous, nonlinear, and
anisotropic materials, as well as permanent magnets. The main results are
proven on the continuous level, but they carry over almost verbatim to various
approximation schemes, including finite elements and isogeometric analysis,
leading to bounds on the iteration numbers, which are independent of the
particular discretization. The theoretical results are illustrated by numerical
tests for a typical benchmark problem.
