Communications in Mathematical Sciences
Volume 15 (2017)
Little-$o$ convergence rates for several alternating minimization methods
Pages: 197 – 211
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