SOC-convexity and SOC-monotonity

Jein Shan Chen*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapter


In this chapter, we introduce the SOC-convexity and SOC-monotonicity which are natural extensions of traditional convexity and monotonicity. These kinds of SOC-convex and SOC-monotone functions are also parallel to matrix-convex and matrix-monotone functions, see [21, 74]. We start with studying the SOC-convexity and SOC-monotonicity for some simple functions, e.g., f(t)=t 2 , t 3 ,1/t,t 1/2 , |t| and [t]+. Then, we explore characterizations of SOC-convex and SOC-monotone functions.

Original languageEnglish
Title of host publicationSpringer Optimization and Its Applications
PublisherSpringer International Publishing
Number of pages61
Publication statusPublished - 2019

Publication series

NameSpringer Optimization and Its Applications
ISSN (Print)1931-6828
ISSN (Electronic)1931-6836

ASJC Scopus subject areas

  • Control and Optimization


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