Submitted

Accelerated Gradient and Skew-Symmetric Splitting Methods for a Class of Monotone Operator Equations

Long Chen and Jingrong Wei

Submitted

arXiv   Bibtex coming soon

ABSTRACT:

 A class of monotone operator equations, which can be
decomposed into sum of the 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 converge in linear rates. 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, a linear convergent method with optimal lower
iteration complexity is proposed. The robustness and efficiency of GSS
and AGSS methods are verified via extensive numerical experiments.