Symmetric cone monotone functions and symmetric cone convex functions

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    4 Citations (Scopus)

    Abstract

    Symmetric cone (SC) monotone functions and SC-convex functions are real scalar valued functions which induce Löwner operators associated with a simple Euclidean Jordan algebra to preserve the monotone order and convex order, respectively. In this paper, for a general simple Euclidean Jordan algebra except for octonion case, we show that the SC-monotonicity (respectively, SC-convexity) of order r is implied by the matrix monotonicity (respectively, matrix convexity) of some fixed order r' (≥ r). As a consequence, we draw the conclusion that (except for octonion case) a function is SC-monotone (respectively, SC-convex) if and only if it is matrix monotone (respectively, matrix convex).

    Original languageEnglish
    Pages (from-to)499-512
    Number of pages14
    JournalJournal of Nonlinear and Convex Analysis
    Volume17
    Issue number3
    Publication statusPublished - 2016 Jan 1

    Keywords

    • Euclidean Jordan algebra
    • Lowner operator
    • Matrix-monotone
    • SC-convex
    • SC-monotone
    • Symmetric cone

    ASJC Scopus subject areas

    • Analysis
    • Geometry and Topology
    • Control and Optimization
    • Applied Mathematics

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