Convexity of sets and quadratic functions on the hyperbolic space
Optimization and Control
2022-07-13 v4
Abstract
In this paper some concepts of convex analysis on hyperbolic space are studied. We first study properties of the intrinsic distance, for instance, we present the spectral decomposition of its Hessian. Next, we study the concept of convex sets and the intrinsic projection onto these sets. We also study the concept of convex functions and present first and second order characterizations of these functions, as well as some optimization concepts related to them. An extensive study of the hyperbolically convex quadratic functions is also presented.
Keywords
Cite
@article{arxiv.2110.06514,
title = {Convexity of sets and quadratic functions on the hyperbolic space},
author = {Orizon Pereira Ferreira and Sándor Zoltán Németh and Jinzhen Zhu},
journal= {arXiv preprint arXiv:2110.06514},
year = {2022}
}