Smoothness Parameter of Power of Euclidean Norm

Anton Rodomanov () and Yurii Nesterov ()
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Anton Rodomanov: Catholic University of Louvain
Yurii Nesterov: Catholic University of Louvain

Journal of Optimization Theory and Applications, 2020, vol. 185, issue 2, No 1, 303-326

Abstract: Abstract In this paper, we study derivatives of powers of Euclidean norm. We prove their Hölder continuity and establish explicit expressions for the corresponding constants. We show that these constants are optimal for odd derivatives and at most two times suboptimal for the even ones. In the particular case of integer powers, when the Hölder continuity transforms into the Lipschitz continuity, we improve this result and obtain the optimal constants.

Keywords: Hölder continuity; Polynomials; Optimal constants; 26A16; 46G05; 11C08 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10957-020-01653-6

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