Convexity of Sets and Quadratic Functions on the Hyperbolic Space.

Autor:	Ferreira, Orizon P., Németh, Sándor Z., Zhu, Jinzhen
Předmět:	HYPERBOLIC spaces HYPERBOLIC functions FUNCTION spaces SET functions CONVEX sets CONVEXITY spaces
Zdroj:	Journal of Optimization Theory & Applications; Jul2024, Vol. 202 Issue 1, p421-455, 35p
Abstrakt:	In this paper, some concepts of convex analysis on hyperbolic spaces 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. [ABSTRACT FROM AUTHOR]
Databáze:	Complementary Index
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