LAUSR

In a series of papers (Solodov and Svaiter in J Convex Anal 6(1):59–70, 1999; Set-Valued Anal 7(4):323–345, 1999; Numer Funct Anal Optim 22(7–8):1013–1035, 2001) Solodov and Svaiter introduced new inexact variants of the proximal point method with relative error tolerances. Point-wise and ergodic iteration-complexity bounds for one of these methods, namely the hybrid proximal extragradient method (1999) were established by Monteiro and Svaiter (SIAM J Optim 20(6):2755–2787, 2010). Here, we extend these results to a more general framework, by establishing point-wise and ergodic iteration-complexity bounds for the inexact proximal point method studied by Solodov and Svaiter (2001). Using this framework we derive global convergence results and iteration-complexity bounds for a family of projective splitting methods for solving monotone inclusion problems, which generalize the projective splitting methods introduced and studied by Eckstein and Svaiter (SIAM J Control Optim 48(2):787–811, 2009).