Variable Quasi-Bregman Monotone Sequences

Abstract

We introduce a notion of variable quasi-Bregman monotone sequence which unifies the notion of variable metric quasi-Fej\'er monotone sequences and that of Bregman monotone sequences. The results are applied to analyze the asymptotic behavior of proximal iterations based on variable Bregman distance and of algorithms for solving convex feasibility problems in reflexive real Banach spaces.