The Glowinski–Le Tallec splitting method revisited: A general convergence and convergence rate analysis

In this paper, we focus on a splitting method called the $ \theta $-scheme proposed by Glowinski and Le Tallec in [17,20,27]. First, present an elaborative convergence analysis Hilbert space propose general convergent inexact $-scheme. Second, for unconstrained problems, prove of show sublinear rate terms objective value. Furthermore, practical is derived to solve l_2 $-loss based problems its proved. Third, constrained even though available literature, yet unknown until provide one via variational reformulation solution set. Besides, order relax condition imposed $-scheme, new variant convergence. Finally, some preliminary numerical experiments demonstrate efficiency our methods.