Averaged alternating reflections in geodesic spaces
Optimization and Control
2013-10-03 v3 Metric Geometry
Abstract
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 feasibility problem for two sets in a nonlinear context. We show that weak convergence results from Hilbert spaces find natural counterparts in spaces of constant curvature. Moreover, in this particular setting, one obtains strong convergence.
Cite
@article{arxiv.1211.4958,
title = {Averaged alternating reflections in geodesic spaces},
author = {Aurora Fernandez-Leon and Adriana Nicolae},
journal= {arXiv preprint arXiv:1211.4958},
year = {2013}
}
Comments
13 pages; some typos corrected