SOC-monotone and SOC-convex functions vs. matrix-monotone and matrix-convex functions

Shaohua Pan, Yungyen Chiang, Jein Shan Chen*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


The SOC-monotone function (respectively, SOC-convex function) is a scalar valued function that induces a map to preserve the monotone order (respectively, the convex order), when imposed on the spectral factorization of vectors associated with second-order cones (SOCs) in general Hilbert spaces. In this paper, we provide the sufficient and necessary characterizations for the two classes of functions, and particularly establish that the set of continuous SOC-monotone (respectively, SOC-convex) functions coincides with that of continuous matrix monotone (respectively, matrix convex) functions of order 2.

Original languageEnglish
Pages (from-to)1264-1284
Number of pages21
JournalLinear Algebra and Its Applications
Issue number5
Publication statusPublished - 2012 Sept 1


  • Hilbert space
  • SOC-convexity
  • SOC-monotonicity
  • Second-order cone

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics


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