5 citations · 15 across the 13 of their papers we have counts for
7 papers · 1 filter
Basic convex analysis in metric spaces with bounded curvature
Adrian S. Lewis, Genaro López-Acedo, Adriana Nicolae
Differentiable structure ensures that many of the basics of classical convex analysis extend naturally from Euclidean space to Riemannian manifolds. Without such structure, however…
Local linear convergence of alternating projections in metric spaces with bounded curvature
Adrian S. Lewis, Genaro López-Acedo, Adriana Nicolae
We consider the popular and classical method of alternating projections for finding a point in the intersection of two closed sets. By situating the algorithm in a metric space, eq…
"Lion-Man" and the Fixed Point Property
Genaro López-Acedo, Adriana Nicolae, Bożena Piątek
This paper focuses on the relation between the fixed point property for continuous mappings and a discrete lion and man game played in a strongly convex domain. Our main result sta…
An abstract proximal point algorithm
Laurentiu Leustean, Adriana Nicolae, Andrei Sipos
The proximal point algorithm is a widely used tool for solving a variety of convex optimization problems such as finding zeros of maximally monotone operators, fixed points of none…
Moduli of regularity and rates of convergence for Fejér monotone sequences
Ulrich Kohlenbach, Genaro López-Acedo, Adriana Nicolae
In this paper we introduce the concept of modulus of regularity as a tool to analyze the speed of convergence, including the finite termination, for classes of Fejér monotone seque…
Proximal minimization in CAT spaces
Rafa Espínola, Adriana Nicolae
In this note, we provide convergence results for the proximal point algorithm and a splitting variant thereof in the setting of CAT spaces with using a recent definitio…
Averaged alternating reflections in geodesic spaces
Aurora Fernandez-Leon, Adriana Nicolae
We study the nonexpansivity of reflection mappings in geodesic spaces and apply our findings to the averaged alternating reflection algorithm employed in solving the convex feasibi…