The vector-valued functions associated with circular cones
type: Item
instance of: scholarly article
title: The vector-valued functions associated with circular cones
zbMATH Open document ID: 1474.49035
DOI: 10.1155/2014/603542
author: Jein-Shan Chen
author: Jinchuan Zhou
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: 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 \(\mathcal{L}_\theta\) denote the circular cone in \(\mathbb{R}^n\). For a function \(f\) from \(\mathbb{R}\) to \(\mathbb{R}\), one can define a corresponding vector-valued function \(f^{\mathcal{L}_\theta}\) on \(\mathbb{R}^n\) by applying \(f\) to the spectral values of the spectral decomposition of \(x \in \mathbb{R}^n\) with respect to \(\mathcal{L}_\theta\). In this paper, we study properties that this vector-valued function inherits from \(f\), including Hölder continuity, \(B\)-subdifferentiability, \(\rho\)-order semismoothness, and positive homogeneity. These results will play crucial role in designing solution methods for optimization problem involved in circular cone constraints.
Mathematics Subject Classification ID: 49J52
Mathematics Subject Classification ID: 90C22
zbMATH DE Number: 7022706
Wikidata QID: Q59039884
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/603542
OpenAlex ID: W1969517291
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description: scientific article; zbMATH DE number 7022706