  The constrained minimization (respectively maximization) of directed
distances and of related generalized entropies is a fundamental task in
information theory as well as in the adjacent fields of statistics, machine
learning, artificial intelligence, signal processing and pattern recognition.
In our previous paper "A precise bare simulation approach to the minimization
of some distances. I. Foundations", we obtained such kind of constrained optima
by a new dimension-free precise bare (pure) simulation method, provided
basically that (i) the underlying directed distance is of f-divergence type,
and that (ii) this can be connected to a light-tailed probability distribution
in a certain manner. In the present paper, we extend this approach such that
constrained optimization problems of a very huge amount of directed distances
and generalized entropies -- and beyond -- can be tackled by a newly developed
dimension-free extended bare simulation method, for obtaining both optima as
well as optimizers. Almost no assumptions (like convexity) on the set of
constraints are needed, within our discrete setup of arbitrary dimension, and
our method is precise (i.e., converges in the limit). For instance, we cover
constrained optimizations of arbitrary f-divergences, Bregman distances, scaled
Bregman distances and weighted Euclidean distances. The potential for
wide-spread applicability is indicated, too; in particular, we deliver many
recent references for uses of the involved distances/divergences in various
different research fields (which may also serve as an interdisciplinary
interface).
