  This paper presents a nonsmooth proximal point technique for convex
optimization in a special class of Hadamard manifold called homogeneous domains
of positivity. The method is based on the particularization of the Rham
decomposition theorem to symmetric spaces and it is applicable to the computing
of minimizers for convex functions. Homogeneous domains of positivity to be
considered in this work are those of specially reducible type in a sense which
is introduced and largely discussed along the paper. General aspects on the
technique are shown as the convergence analysis to the inner iterations of the
method, the global convergence for both versions exact and inexact and, under
particular assumptions, a lower bound to the number of outer iterations of the
inexact version.
