Abstract and Applied Analysis

The Vector-Valued Functions Associated with Circular Cones

Jinchuan Zhou and Jein-Shan Chen

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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 L θ denote the circular cone in R n . For a function f from R to R , one can define a corresponding vector-valued function f L θ on R n by applying f to the spectral values of the spectral decomposition of x R n with respect to L θ . 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.

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 603542, 21 pages.

Dates
First available in Project Euclid: 6 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412606019

Digital Object Identifier
doi:10.1155/2014/603542

Mathematical Reviews number (MathSciNet)
MR3228078

Zentralblatt MATH identifier
07022706

Citation

Zhou, Jinchuan; Chen, Jein-Shan. The Vector-Valued Functions Associated with Circular Cones. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 603542, 21 pages. doi:10.1155/2014/603542. https://projecteuclid.org/euclid.aaa/1412606019


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