This article presents the geometry and optimal problems associated to the barrier function
method on affine manifolds. The crucial ideas include:(i) new properties regarding the …

In our paper [1], we introduced a new class of self-concordant functions, defined on
Riemannian manifolds endowed with metrics of diagonal type. The aim of this note is …

A Finsler manifold is a differential manifold together with a Finsler metric, in this paper we
construct a new class of Finsler metric affine mainfolds on bilevel semivectorial with …

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 …

Our original results refer to dualistic structure on primaldual interior-point methods for
symmetric cone programs with linear constraints. It is shown that scalings by the Nesterov …