Communications in Mathematical Sciences

Volume 15 (2017)

Number 1

Little-$o$ convergence rates for several alternating minimization methods

Pages: 197 – 211



Tao Sun (College of Science, National University of Defense Technology, Changsha, Hunan, China)

Lizhi Cheng (College of Science and the State Key Laboratory for High Performance Computation, National University of Defense Technology, Changsha, Hunan, China)


Alternating minimization is an efficient method for solving convex minimization problems whose objective function is a sum of a differentiable function and a separable nonsmooth function. Variants and extensions of the alternating minimization method have been developed in recent years. In this paper, we consider the convergence rate of several existing alternating minimization schemes. We improve the proven big-$O$ convergence rate of these algorithms to little-$o$ under an error bound condition which is actually quite common in many applications. We also investigate the convergence of a variant of alternating minimization proposed in this paper.


alternating minimizations, little-o convergence rate, error bound

2010 Mathematics Subject Classification

47N10, 90C26, 90C30

Published 10 January 2017