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Randomness and Differentiability of Convex Functions

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Evolving Computability (CiE 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9136))

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Abstract

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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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Auckland, Auckland, New Zealand

    Alex Galicki

Authors
  1. Alex Galicki
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Correspondence to Alex Galicki .

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Editors and Affiliations

  1. Department of Computer Science, Swansea University, Swansea, United Kingdom

    Arnold Beckmann

  2. University of Bucharest, Bucharest, Romania

    Victor Mitrana

  3. Sofia University, Sofia, Bulgaria

    Mariya Soskova

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Galicki, A. (2015). Randomness and Differentiability of Convex Functions. In: Beckmann, A., Mitrana, V., Soskova, M. (eds) Evolving Computability. CiE 2015. Lecture Notes in Computer Science(), vol 9136. Springer, Cham. https://doi.org/10.1007/978-3-319-20028-6_20

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  • DOI: https://doi.org/10.1007/978-3-319-20028-6_20

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-20027-9

  • Online ISBN: 978-3-319-20028-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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