A hybrid proximal-extragradient algorithm with inertial effects

2014/07/01 by Bot, Radu Ioan, Csetnek, Ernö Robert
#47H05 #65K05 #90C25 #FOS: Mathematics #Functional Analysis (math.FA) #Numerical Analysis (math.NA) #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1407.0214

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 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 in the framework of the proposed iterative scheme.

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