SOC-Convexity and SOC-Monotonity

  • Jein-Shan ChenEmail author
Part of the Springer Optimization and Its Applications book series (SOIA, volume 143)


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.

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Department of MathematicsNational Taiwan Normal UniversityTaipeiTaiwan

Personalised recommendations