  In this paper, we study the global convergence of majorization minimization
(MM) algorithms for solving nonconvex regularized optimization problems. MM
algorithms have received great attention in machine learning. However, when
applied to nonconvex optimization problems, the convergence of MM algorithms is
a challenging issue. We introduce theory of the Kurdyka- Lojasiewicz inequality
to address this issue. In particular, we show that many nonconvex problems
enjoy the Kurdyka- Lojasiewicz property and establish the global convergence
result of the corresponding MM procedure. We also extend our result to a well
known method that called CCCP (concave-convex procedure).
