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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The slope robustly determines convex functions
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by Aris Daniilidis and Dmitriy Drusvyatskiy
Proc. Amer. Math. Soc. 151 (2023), 4751-4756
DOI: https://doi.org/10.1090/proc/16503
Published electronically: July 14, 2023

Abstract:

We show that the deviation between the slopes of two convex functions controls the deviation between the functions themselves. This result reveals that the slope—a one dimensional construct—robustly determines convex functions, up to a constant of integration.
References
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Bibliographic Information
  • Aris Daniilidis
  • Affiliation: VADOR E105-04, Institute of Statistics and Mathematical Methods in Economics, TU Wien, Wiedner Hauptstraße 8, A-1040 Wien, Austria
  • MR Author ID: 613204
  • ORCID: 0000-0003-4837-694X
  • Email: aris.daniilidis@tuwien.ac.at
  • Dmitriy Drusvyatskiy
  • Affiliation: Department of Mathematics, University of Washington, C-138 Padelford, Seattle, Washington 98195
  • MR Author ID: 932389
  • Email: ddrusv@uw.edu
  • Received by editor(s): December 5, 2022
  • Received by editor(s) in revised form: March 13, 2023
  • Published electronically: July 14, 2023
  • Additional Notes: The first author acknowledges support from the Austrian Science Fund (FWF, P-36344-N)
    The work of the second author was supported by the NSF DMS 1651851 and CCF 1740551 awards
  • Communicated by: Ryan Hynd
  • © Copyright 2023 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 151 (2023), 4751-4756
  • MSC (2020): Primary 26B25, 49K40; Secondary 37C10, 49J52
  • DOI: https://doi.org/10.1090/proc/16503
  • MathSciNet review: 4634878