2021/10/13 by O. P. Ferreira, Ferreira, Orizon Pereira, S. Z. Németh +3
Mathematics · Computer Science · #Functional Equations Stability Results #Optimization and Variational Analysis #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.2110.06514
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.