  A class of monotone operator equations, which can be decomposed into sum of a
gradient of a strongly convex function and a linear and skew-symmetric
operator, is considered in this work. Based on discretization of the
generalized gradient flow, gradient and skew-symmetric splitting (GSS) methods
are proposed and proved to convergent in linear rate. To further accelerate the
convergence, an accelerated gradient flow is proposed and accelerated gradient
and skew-symmetric splitting (AGSS) methods are developed, which extends the
acceleration among the existing works on the convex minimization to a more
general class of monotone operator equations. In particular, when applied to
smooth saddle point systems with bilinear coupling, an accelerated transformed
primal-dual (ATPD) method is proposed and shown to achieve linear rates with
optimal lower iteration complexity.

Optimization and Control