Abstract and Applied Analysis
- Abstr. Appl. Anal.
- Volume 2014, Special Issue (2014), Article ID 603542, 21 pages.
The Vector-Valued Functions Associated with Circular Cones
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 denote the circular cone in . For a function from to , one can define a corresponding vector-valued function on by applying to the spectral values of the spectral decomposition of with respect to . In this paper, we study properties that this vector-valued function inherits from , including Hölder continuity, -subdifferentiability, -order semismoothness, and positive homogeneity. These results will play crucial role in designing solution methods for optimization problem involved in circular cone constraints.
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 603542, 21 pages.
First available in Project Euclid: 6 October 2014
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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