  State-of-the-art methods for solving smooth optimization problems are
nonlinear conjugate gradient, low memory BFGS, and Majorize-Minimize (MM)
subspace algorithms. The MM subspace algorithm which has been introduced more
recently has shown good practical performance when compared with other methods
on various optimization problems arising in signal and image processing.
However, to the best of our knowledge, no general result exists concerning the
theoretical convergence rate of the MM subspace algorithm. This paper aims at
deriving such convergence rates both for batch and online versions of the
algorithm and, in particular, discusses the influence of the choice of the
subspace.
