  Large-scale nonconvex and nonsmooth problems have attracted considerable
attention in the fields of compress sensing, big data optimization and machine
learning. Exploring effective methods is still the main challenge of today's
research. Stochastic coordinate descent type methods have been widely used to
solve large-scale optimization problems. In this paper, we derive the
convergence of variable Bregman stochastic coordinate descent (VBSCD) method
for a broad class of nonsmooth and nonconvex optimization problems, i.e., any
accumulation of the sequence generated by VBSCD is almost surely a critical
point. Moreover, we develop a new variational approach on level sets that aim
towards the convergence rate analysis. If the level-set subdifferential error
bound holds, we derive a linear rate of convergence for the expected values of
the objective function and expected values of random variables generated by
VBSCD.
