The vector-valued functions associated with circular cones

Jinchuan Zhou, Jein-Shan Chen

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

The circular cone is a pointed closed convex cone having hyperspherical sections orthogonal to its axis of revolution about which the cone is invariant to rotation, which includes second-order cone as a special case when the rotation angle is 45 degrees. Let Lθ denote the circular cone in Rn. For a function f from R to R, one can define a corresponding vector-valued function fLθ on Rn by applying f to the spectral values of the spectral decomposition of x Rn with respect to Lθ. In this paper, we study properties that this vector-valued function inherits from f, including Hölder continuity, B-subdifferentiability, ρ-order semismoothness, and positive homogeneity. These results will play crucial role in designing solution methods for optimization problem involved in circular cone constraints.

Original language English 603542 Abstract and Applied Analysis 2014 https://doi.org/10.1155/2014/603542 Published - 2014 Jan 1

Fingerprint

Circular cone
Vector-valued Functions
Cones
Semismoothness
Cone Constraints
Second-order Cone
Spectral Decomposition
Convex Cone
Homogeneity
Cone
Optimization Problem
Denote
Angle
Closed
Invariant
Decomposition

ASJC Scopus subject areas

• Analysis
• Applied Mathematics

Cite this

In: Abstract and Applied Analysis, Vol. 2014, 603542, 01.01.2014.

Research output: Contribution to journalArticle

@article{6bc579a6aef04ba592017f421ec90171,
title = "The vector-valued functions associated with circular cones",
abstract = "The circular cone is a pointed closed convex cone having hyperspherical sections orthogonal to its axis of revolution about which the cone is invariant to rotation, which includes second-order cone as a special case when the rotation angle is 45 degrees. Let Lθ denote the circular cone in Rn. For a function f from R to R, one can define a corresponding vector-valued function fLθ on Rn by applying f to the spectral values of the spectral decomposition of x Rn with respect to Lθ. In this paper, we study properties that this vector-valued function inherits from f, including H{\"o}lder continuity, B-subdifferentiability, ρ-order semismoothness, and positive homogeneity. These results will play crucial role in designing solution methods for optimization problem involved in circular cone constraints.",
author = "Jinchuan Zhou and Jein-Shan Chen",
year = "2014",
month = "1",
day = "1",
doi = "10.1155/2014/603542",
language = "English",
volume = "2014",
journal = "Abstract and Applied Analysis",
issn = "1085-3375",
publisher = "Hindawi Publishing Corporation",

}

TY - JOUR

T1 - The vector-valued functions associated with circular cones

AU - Zhou, Jinchuan

AU - Chen, Jein-Shan

PY - 2014/1/1

Y1 - 2014/1/1

N2 - The circular cone is a pointed closed convex cone having hyperspherical sections orthogonal to its axis of revolution about which the cone is invariant to rotation, which includes second-order cone as a special case when the rotation angle is 45 degrees. Let Lθ denote the circular cone in Rn. For a function f from R to R, one can define a corresponding vector-valued function fLθ on Rn by applying f to the spectral values of the spectral decomposition of x Rn with respect to Lθ. In this paper, we study properties that this vector-valued function inherits from f, including Hölder continuity, B-subdifferentiability, ρ-order semismoothness, and positive homogeneity. These results will play crucial role in designing solution methods for optimization problem involved in circular cone constraints.

AB - The circular cone is a pointed closed convex cone having hyperspherical sections orthogonal to its axis of revolution about which the cone is invariant to rotation, which includes second-order cone as a special case when the rotation angle is 45 degrees. Let Lθ denote the circular cone in Rn. For a function f from R to R, one can define a corresponding vector-valued function fLθ on Rn by applying f to the spectral values of the spectral decomposition of x Rn with respect to Lθ. In this paper, we study properties that this vector-valued function inherits from f, including Hölder continuity, B-subdifferentiability, ρ-order semismoothness, and positive homogeneity. These results will play crucial role in designing solution methods for optimization problem involved in circular cone constraints.

UR - http://www.scopus.com/inward/record.url?scp=84904159836&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84904159836&partnerID=8YFLogxK

U2 - 10.1155/2014/603542

DO - 10.1155/2014/603542

M3 - Article

VL - 2014

JO - Abstract and Applied Analysis

JF - Abstract and Applied Analysis

SN - 1085-3375

M1 - 603542

ER -