  We revisit the operator splitting schemes proposed in a recent work of [Some
extensions of the operator splitting schemes based on Lagrangian and
primal-dual: A unified proximal point analysis, Feng Xue, Optimization, 2022,
doi: 10.1080/02331934.2022.2057309], and further analyze the convergence of the
generalized Bregman distance and the primal-dual gap of these algorithms within
a unified proximal point framework. The possibility of reduction to a simple
resolvent is also discussed by exploiting the structure and possible degeneracy
of the underlying metric.
