Convexity of sets and quadratic functions on the hyperbolic space

Orizon Ferreira; Sandor Nemeth; Jinzhen Zhu

doi:10.1007/s10957-022-02073-4

Convexity of sets and quadratic functions on the hyperbolic space

Orizon Ferreira, Sandor Nemeth, Jinzhen Zhu

Mathematics

Research output: Contribution to journal › Article › peer-review

17 Downloads (Pure)

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.

Original language	English
Journal	Journal of Optimization Theory and Applications
Volume	2022
DOIs	https://doi.org/10.1007/s10957-022-02073-4
Publication status	Published - 12 Jul 2022

Bibliographical note

Not yet published as of 11/07/2022.

Keywords

Convex cone
Convex function
Convex set
Hyperbolic space
Quadratic Function

Access to Document

10.1007/s10957-022-02073-4Licence: None: All rights reserved

FerreiraO2022Convexity
This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: https://doi.org/10.1007/s10957-022-02073-4
Accepted author manuscript, 233 KBLicence: Other (please specify with Rights Statement)

Cite this

@article{e3873edbec0e45f39499026caf20d0db,

title = "Convexity of sets and quadratic functions on the hyperbolic space",

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 = "Convex cone, Convex function, Convex set, Hyperbolic space, Quadratic Function",

author = "Orizon Ferreira and Sandor Nemeth and Jinzhen Zhu",

note = "Not yet published as of 11/07/2022.",

year = "2022",

month = jul,

day = "12",

doi = "10.1007/s10957-022-02073-4",

language = "English",

volume = "2022",

journal = "Journal of Optimization Theory and Applications",

issn = "0022-3239",

publisher = "Springer",

}

TY - JOUR

T1 - Convexity of sets and quadratic functions on the hyperbolic space

AU - Ferreira, Orizon

AU - Nemeth, Sandor

AU - Zhu, Jinzhen

N1 - Not yet published as of 11/07/2022.

PY - 2022/7/12

Y1 - 2022/7/12

N2 - 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.

AB - 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.

KW - Convex cone

KW - Convex function

KW - Convex set

KW - Hyperbolic space

KW - Quadratic Function

UR - http://www.scopus.com/inward/record.url?scp=85134296851&partnerID=8YFLogxK

U2 - 10.1007/s10957-022-02073-4

DO - 10.1007/s10957-022-02073-4

M3 - Article

SN - 0022-3239

VL - 2022

JO - Journal of Optimization Theory and Applications

JF - Journal of Optimization Theory and Applications

ER -

Convexity of sets and quadratic functions on the hyperbolic space

Abstract

Bibliographical note

Keywords

Access to Document

Fingerprint

Cite this