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

Shaohua Pan, Yungyen Chiang, Jein-Shan Chen

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

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
Volume437
Issue number5
DOIs
Publication statusPublished - 2012 Sep 1

Fingerprint

Monotone Matrix
Second-order Cone
Matrix Function
Convex function
Cones
Monotone
Convex Order
Spectral Factorization
Monotone Function
Hilbert spaces
Set theory
Factorization
Hilbert space
Scalar
Sufficient
Necessary

Keywords

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

ASJC Scopus subject areas

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

Cite this

SOC-monotone and SOC-convex functions vs. matrix-monotone and matrix-convex functions. / Pan, Shaohua; Chiang, Yungyen; Chen, Jein-Shan.

In: Linear Algebra and Its Applications, Vol. 437, No. 5, 01.09.2012, p. 1264-1284.

Research output: Contribution to journalArticle

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