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The Vector-Valued Functions Associated with Circular Cones

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  • Jinchuan Zhou
  • Jein-Shan Chen

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.

Suggested Citation

  • Jinchuan Zhou & Jein-Shan Chen, 2014. "The Vector-Valued Functions Associated with Circular Cones," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-21, June.
    • Handle: RePEc:hin:jnlaaa:603542
    DOI: 10.1155/2014/603542
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