  The paper presents primal-dual proximal splitting methods for convex
optimization, in which generalized Bregman distances are used to define the
primal and dual proximal update steps. The methods extend the primal and dual
Condat-Vu algorithms and the primal-dual three-operator (PD3O) algorithm. The
Bregman extensions of the Condat-Vu algorithms are derived from the Bregman
proximal point method applied to a monotone inclusion problem. Based on this
interpretation, a unified framework for the convergence analysis of the two
methods is presented. We also introduce a line search procedure for stepsize
selection in the Bregman dual Condat-Vu algorithm applied to
equality-constrained problems. Finally, we propose a Bregman extension of PD3O
and analyze its convergence.
