A Hybrid Proximal-Extragradient Algorithm with Inertial Effects

Abstract

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.

Keywords:

• Enlargement of a maximally monotone operator
• Hybrid proximal point algorithm
• Inertial splitting algorithm
• Maximally monotone operator
• Resolvent

Mathematics Subject Classification:

• 47H05
• 65K05
• 90C25