SOC-convexity and SOC-monotonity

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

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
Pages39-99
Number of pages61
DOIs
Publication statusPublished - 2019 Jan 1

Publication series

NameSpringer Optimization and Its Applications
Volume143
ISSN (Print)1931-6828
ISSN (Electronic)1931-6836

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ASJC Scopus subject areas

  • Control and Optimization

Cite this

Chen, J. S. (2019). SOC-convexity and SOC-monotonity. In Springer Optimization and Its Applications (pp. 39-99). (Springer Optimization and Its Applications; Vol. 143). Springer International Publishing. https://doi.org/10.1007/978-981-13-4077-2_2