6 research outputs found
Randomized Bregman Coordinate Descent Methods for Non-Lipschitz Optimization
We propose a new \textit{randomized Bregman (block) coordinate descent}
(RBCD) method for minimizing a composite problem, where the objective function
could be either convex or nonconvex, and the smooth part are freed from the
global Lipschitz-continuous (partial) gradient assumption. Under the notion of
relative smoothness based on the Bregman distance, we prove that every limit
point of the generated sequence is a stationary point. Further, we show that
the iteration complexity of the proposed method is to
achieve -stationary point, where is the number of blocks of
coordinates. If the objective is assumed to be convex, the iteration complexity
is improved to . If, in addition, the objective is strongly
convex (relative to the reference function), the global linear convergence rate
is recovered. We also present the accelerated version of the RBCD method, which
attains an iteration complexity for the convex
case, where the scalar is determined by the
\textit{generalized translation variant} of the Bregman distance. Convergence
analysis without assuming the global Lipschitz-continuous (partial) gradient
sets our results apart from the existing works in the composite problems.Comment: First draf