TY - CHAP
T1 - SOC-convexity and SOC-monotonity
AU - Chen, Jein Shan
N1 - Publisher Copyright:
© Springer Nature Singapore Pte Ltd. 2019.
PY - 2019
Y1 - 2019
N2 - 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.
AB - 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.
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U2 - 10.1007/978-981-13-4077-2_2
DO - 10.1007/978-981-13-4077-2_2
M3 - Chapter
AN - SCOPUS:85062681293
T3 - Springer Optimization and Its Applications
SP - 39
EP - 99
BT - Springer Optimization and Its Applications
PB - Springer International Publishing
ER -