3 research outputs found
Iteration Complexity of Randomized Primal-Dual Methods for Convex-Concave Saddle Point Problems
In this paper we propose a class of randomized primal-dual methods to contend
with large-scale saddle point problems defined by a convex-concave function
. We analyze the convergence rate of the
proposed method under the settings of mere convexity and strong convexity in
-variable. In particular, assuming is
Lipschitz and is coordinate-wise Lipschitz for
any fixed , the ergodic sequence generated by the algorithm achieves the
convergence rate of in a suitable error metric where
denotes the number of coordinates for the primal variable. Furthermore,
assuming that is uniformly strongly convex for any ,
and that is linear in , the scheme displays convergence rate
of . We implemented the proposed algorithmic framework to
solve kernel matrix learning problem, and tested it against other
state-of-the-art solvers