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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 Lθ denote the circular cone in Rn. For a function f from R to R, one can define a corresponding vector‐valued function fLθ on Rn by applying f to the spectral values of the spectral decomposition of x∈Rn with respect to Lθ. 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.

Suggested Citation

  • Jinchuan Zhou & Jein-Shan Chen, 2014. "The Vector‐Valued Functions Associated with Circular Cones," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:603542
    DOI: 10.1155/2014/603542
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    References listed on IDEAS

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    1. Liqun Qi, 1993. "Convergence Analysis of Some Algorithms for Solving Nonsmooth Equations," Mathematics of Operations Research, INFORMS, vol. 18(1), pages 227-244, February.
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