# Symmetric cone monotone functions and symmetric cone convex functions

Research output: Contribution to journalArticle

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 language English 499-512 14 Journal of Nonlinear and Convex Analysis 17 3 Published - 2016

### Fingerprint

Symmetric Cone
Monotone Function
Convex function
Cones
Euclidean Jordan Algebra
Octonions
Algebra
Monotonicity
Convexity
Monotone
Monotone Matrix
Convex Order
Mathematical operators
Scalar
If and only if
Operator

### 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

### Cite this

In: Journal of Nonlinear and Convex Analysis, Vol. 17, No. 3, 2016, p. 499-512.

Research output: Contribution to journalArticle

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