Convexity of Sets and Quadratic Functions on the Hyperbolic Space

Orizon P. Ferreira (), Sándor Z. Németh () and Jinzhen Zhu ()
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Orizon P. Ferreira: IME, Universidade Federal de Goiás
Sándor Z. Németh: University of Birmingham
Jinzhen Zhu: University of Birmingham

Journal of Optimization Theory and Applications, 2024, vol. 202, issue 1, No 19, 455 pages

Abstract: Abstract 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.

Keywords: Hyperbolic space; Convex cone; Convex set; Convex function; Quadratic function; 90C30; 90C26 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10957-022-02073-4

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