  The principle of majorization-minimization (MM) provides a general framework
for eliciting effective algorithms to solve optimization problems. However,
they often suffer from slow convergence, especially in large-scale and
high-dimensional data settings. This has drawn attention to acceleration
schemes designed exclusively for MM algorithms, but many existing designs are
either problem-specific or rely on approximations and heuristics loosely
inspired by the optimization literature. We propose a novel, rigorous
quasi-Newton method for accelerating any valid MM algorithm, cast as seeking a
fixed point of the MM \textit{algorithm map}. The method does not require
specific information or computation from the objective function or its gradient
and enjoys a limited-memory variant amenable to efficient computation in
high-dimensional settings. By connecting our approach to Broyden's classical
root-finding methods, we establish convergence guarantees and identify
conditions for linear and super-linear convergence. These results are validated
numerically and compared to peer methods in a thorough empirical study, showing
that it achieves state-of-the-art performance across a diverse range of
problems.
