Convexity  of non-homogeneous quadratic functions on the hyperbolic space

Orizon Ferreira; Sandor Nemeth; Jinzhen Zhu

doi:10.1007/s10957-023-02332-y

Convexity of non-homogeneous quadratic functions on the hyperbolic space

Orizon Ferreira
, Sandor Nemeth^*
, Jinzhen Zhu

^*Corresponding author for this work

Mathematics

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

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Abstract

In this paper some concepts related to the intrinsic convexity of
non-homogeneous quadratic functions on the hyperbolic space are studied. Unlike in the Euclidean space, the study of intrinsic convexity of non-homogeneous quadratic functions in the hyperbolic space is more elaborate than that of homogeneous quadratic functions. Several characterizations that allow the construction of many examples will be presented.

Original language	English
Pages (from-to)	1085-1105
Number of pages	21
Journal	Journal of Optimization Theory and Applications
Volume	199
Issue number	3
Early online date	9 Nov 2023
DOIs	https://doi.org/10.1007/s10957-023-02332-y
Publication status	Published - 1 Dec 2023

Keywords

90C26
90C30
Convex cone
Convex function
Convex set
Hyperbolic space
Non-homogeneous quadratic function

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Cite this

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AU - Nemeth, Sandor

AU - Zhu, Jinzhen

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Y1 - 2023/12/1

N2 - In this paper some concepts related to the intrinsic convexity of non-homogeneous quadratic functions on the hyperbolic space are studied. Unlike in the Euclidean space, the study of intrinsic convexity of non-homogeneous quadratic functions in the hyperbolic space is more elaborate than that of homogeneous quadratic functions. Several characterizations that allow the construction of many examples will be presented.

AB - In this paper some concepts related to the intrinsic convexity of non-homogeneous quadratic functions on the hyperbolic space are studied. Unlike in the Euclidean space, the study of intrinsic convexity of non-homogeneous quadratic functions in the hyperbolic space is more elaborate than that of homogeneous quadratic functions. Several characterizations that allow the construction of many examples will be presented.

KW - 90C26

KW - 90C30

KW - Convex cone

KW - Convex function

KW - Convex set

KW - Hyperbolic space

KW - Non-homogeneous quadratic function

U2 - 10.1007/s10957-023-02332-y

DO - 10.1007/s10957-023-02332-y

M3 - Article

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EP - 1105

JO - Journal of Optimization Theory and Applications

JF - Journal of Optimization Theory and Applications

IS - 3

ER -

Convexity of non-homogeneous quadratic functions on the hyperbolic space

Abstract

Keywords

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