SOC-Convexity and SOC-Monotonity

Jein-Shan Chen ()
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Jein-Shan Chen: National Taiwan Normal University

Chapter Chapter 2 in SOC Functions and Their Applications, 2019, pp 39-99 from Springer

Abstract: 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.

Date: 2019
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DOI: 10.1007/978-981-13-4077-2_2

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