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.
|Title of host publication||Springer Optimization and Its Applications|
|Publisher||Springer International Publishing|
|Number of pages||61|
|Publication status||Published - 2019 Jan 1|
|Name||Springer Optimization and Its Applications|
ASJC Scopus subject areas
- Control and Optimization