MORE ON SELF-CONCORDANT FUNCTIONS ON RIEMANNIAN MANIFOLDS

The aim of this work is to bring together some contributions to the development of the class of self-concordant functions on Riemannian manifolds, emphasizing on the class of self-concordant barriers. Due to their properties, this class of functions is intensively studied to develop interior point methods for convex and nonlinear optimization. The present study comes to complete some of our recent results, published in Balkan J. Geom. Appl., 2009, and Sci. Bull. UPB, Series A: Appl. Math. Phys., 2010 (see [1] and [3]).