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A hybrid proximal-extragradient algorithm with inertial effects (1407.0214v1)
Published 1 Jul 2014 in math.FA, math.NA, and math.OC
Abstract: We incorporate inertial terms in the hybrid proximal-extragradient algorithm and investigate the convergence properties of the resulting iterative scheme designed for finding the zeros of a maximally monotone operator in real Hilbert spaces. The convergence analysis relies on extended Fej\'er monotonicity techniques combined with the celebrated Opial Lemma. We also show that the classical hybrid proximal-extragradient algorithm and the inertial versions of the proximal point, the forward-backward and the forward-backward-forward algorithms can be embedded in the framework of the proposed iterative scheme.