The Vector-Valued Functions Associated with Circular Cones

Jinchuan Zhou and Jein-Shan Chen

Abstract and Applied Analysis, 2014, vol. 2014, 1-21

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 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.

Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:603542

DOI: 10.1155/2014/603542

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