Randomness and Differentiability of Convex Functions

  • Alex GalickiEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9136)


We study first and second derivatives of computable convex functions on \(\mathbb {R}^n\). The main result of the paper is an effective form of Aleksandrov’s Theorem: we show that computable randomness implies twice-differentiability of computable convex functions.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of AucklandAucklandNew Zealand

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