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Convexity of Sets and Quadratic Functions on the Hyperbolic Space.
- Source :
-
Journal of Optimization Theory & Applications . Jul2024, Vol. 202 Issue 1, p421-455. 35p. - Publication Year :
- 2024
-
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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00223239
- Volume :
- 202
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Journal of Optimization Theory & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 178528823
- Full Text :
- https://doi.org/10.1007/s10957-022-02073-4