Convexity of sets and quadratic functions on the hyperbolic space

Orizon Ferreira, Sandor Nemeth, Jinzhen Zhu

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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.
Original languageEnglish
JournalJournal of Optimization Theory and Applications
Publication statusPublished - 12 Jul 2022

Bibliographical note

Not yet published as of 11/07/2022.


  • Convex cone
  • Convex function
  • Convex set
  • Hyperbolic space
  • Quadratic Function


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