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.
Jinchuan Zhou. Jein-Shan Chen. "The Vector-Valued Functions Associated with Circular Cones." Abstr. Appl. Anal. 2014 (SI71) 1 - 21, 2014. https://doi.org/10.1155/2014/603542