A Characterization of Bregman Firmly Nonexpansive Operators Using a New Monotonicity Concept

نویسندگان

  • Jonathan M. Borwein
  • Simeon Reich
  • Shoham Sabach
چکیده

The property of nonexpansivity (1-Lipschitz) is very important in the analysis of many optimization problems. In this paper we study a more general notion of nonexpansivity – Bregman nonexpansivity. We present a characterization of Bregman firmly nonexpansive operators in general reflexive Banach spaces. This characterization allows us to construct Bregman firmly nonexpansive operators explicitly. We provide several examples of such operators with respect to the Boltzmann-Shannon entropy and the Fermi-Dirac entropy in Euclidean spaces. We also compute resolvents with respect to these functions. AMS 2010 Subject Classification: 26B25, 47H05, 47H09, 52A41.

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تاریخ انتشار 2010