Differentiating convex functions constructively | Zendy

Hannes Diener | Zendy; Matthew Hendtlass | Zendy

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Differentiating convex functions constructively

Author(s) -

Hannes Diener,

Matthew Hendtlass

Publication year - 2020

Publication title -

journal of logic and analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.278

H-Index - 4

ISSN - 1759-9008

DOI - 10.4115/jla.2020.12.8

Subject(s) - mathematics , differentiable function , regular polygon , convex function , convex analysis , subderivative , pure mathematics , proper convex function , effective domain , convex optimization , geometry

In classical analysis, both convex functions and increasing functions [0, 1]→ R are differentiable almost everywhere. We will show that constructively, while we can prove this for convex functions, we cannot do so for increasing ones. In doing so we also show that Rademacher’s Theorem and the Alexandrov Theorem are not constructive. 2010 Mathematics Subject Classification 03F60 (primary)

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