A Hybrid Proximal-Extragradient Algorithm with Inertial Effects

By Radu Ioan Bot, Ernö Robert Csetnek. 2014

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In this article, we incorporate inertial terms in the hybrid proximal-extragradient algorithm and investigate the convergence properties of the resulting iterative scheme designed to find the zeros of a maximally monotone operator in real Hilbert spaces. The convergence analysis relies on extended Fejér 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 into the framework of the proposed iterative scheme.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/5fe1c1ec98e8580930d12db988ba712b53f6dafd