On the Global Convergence of Majorization Minimization Algorithms for Nonconvex Optimization Problems
Numerical Analysis
2015-05-01 v2 Optimization and Control
Abstract
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).
Keywords
Cite
@article{arxiv.1504.07791,
title = {On the Global Convergence of Majorization Minimization Algorithms for Nonconvex Optimization Problems},
author = {Yangyang Kang and Zhihua Zhang and Wu-Jun Li},
journal= {arXiv preprint arXiv:1504.07791},
year = {2015}
}