Randomness and Differentiability of Convex Functions

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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