The Hölder continuity of vector-valued function associated with second-order cone

Yu Lin Chang*, Jein Shan Chen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


Let Kn be the Lorentz/second-order cone in IRn. For any function f from IR to IR, one can define a corresponding vector-valued function fsoc (x) on IRn by applying f to the spectral values of the spectral decomposition of x ∈ IRn with respect to Kn. It was shown by J.-S. Chen, X. Chen and P. Tseng in [5] that this vector-valued function inherits from f the properties of continuity, Lipschitz continuity, directional differentiability, Fréchet differentiability, continuous differentiability, as well as semismoothness. In this note, we further show that the Holder continuity of this vector-valued function is also inherited from f. Such property will be useful in designing solution methods for second-order cone programming and second-order cone complementarity problem.

Original languageEnglish
Pages (from-to)135-141
Number of pages7
JournalPacific Journal of Optimization
Issue number1
Publication statusPublished - 2012 Jan


  • Hölder continuity
  • Second-order cone

ASJC Scopus subject areas

  • Control and Optimization
  • Computational Mathematics
  • Applied Mathematics


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