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.
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Chen, JS. (2019). SOC-Convexity and SOC-Monotonity. In: SOC Functions and Their Applications. Springer Optimization and Its Applications, vol 143. Springer, Singapore. https://doi.org/10.1007/978-981-13-4077-2_2
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DOI: https://doi.org/10.1007/978-981-13-4077-2_2
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Publisher Name: Springer, Singapore
Print ISBN: 978-981-13-4076-5
Online ISBN: 978-981-13-4077-2
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