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- W2103359558 abstract "We prove in this paper that a piecewise $C^2$ function $varphi: mathbb{R}^n rightarrow mathbb{R}$ is convex if and only if for every $(x,y) in {rm gph} partialvarphi$, the limiting second-order subdifferential mapping $partial^2 varphi(x,y): mathbb{R}^n rightrightarrows mathbb{R}^n$ has the so-called positive semi-definiteness (PSD) - in analogy with the notion of positive semi-definiteness of symmetric real matrices. As a by-product, characterization for strong convexity of $varphi$ is established." @default.
- W2103359558 created "2016-06-24" @default.
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- W2103359558 date "2011-02-01" @default.
- W2103359558 modified "2023-09-26" @default.
- W2103359558 title "Characterization of Convexity for a Piecewise C2 Function by the Limiting Second-order Subdifferential" @default.
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- W2103359558 doi "https://doi.org/10.11650/twjm/1500406159" @default.
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