“…In particular, those notions were applied to the proximal point algorithm [16,39,99,73], inexact splitting scheme such as forward-backward splitting (and its accelerated variants) [97,112,71,11], Douglas-Rachford [43,44,106,2], three-operator splitting [114], online optimization [31,1,8], and for designing metaalgorithms such as the hybrid approximate extragradient method [99,72,73,4], and "Catalyst" [63,64]. Inexact proximal operations are also closely related to the theory of ε-subdifferentials, introduced in [14], and to their inexact gradient and subgradient methods (see e.g., [98,71,28,29]). Finally, let us mention higher-order proximal methods, that are introduced in [80,81], and also used together with notions for approximating them.…”