We consider the problem of finding a singularity of a differentiable vector field X defined on a
complete Riemannian manifold. We prove a unified result for theexistence and local …

Interior-point methods offer a highly versatile framework for convex optimization that is
effective in theory and practice. A key notion in their theory is that of a self-concordant …

A damped Newton's method to find a singularity of a vector field in Riemannian setting is
presented with global convergence study. It is ensured that the sequence generated by the …

Dini derivatives in Riemannian manifold settings are studied in this paper. In addition, a
characterization for Lipschitz and convex functions defined on Riemannian manifolds and …

A local convergence analysis of Newton's method for finding a singularity of a differentiable
vector field defined on a complete Riemannian manifold, based on the majorant principle, is …

In this paper, we study Newton's method for finding a singularity of a differentiable vector
field defined on a Riemannian manifold. Under the assumption of invertibility of the covariant …

Drawing ideas from differential geometry and optimization, this thesis presents novel
parameterization-based framework to address optimization problems formulated on a …

We consider the task of estimating the relative pose (position and orientation) between a 3D
object and its projection on a 2D image plane from a set of point correspondences. Our …

We present a Gauss-Newton-on-manifold approach for estimating the relative pose (position
and orientation) between a 3D object and its projection on a 2D image plane from a set of …

The notion of self-concordant function on Euclidean spaces was introduced and studied by
Nesterov and Nemirovsky [6]. They have used these functions to design numerical …