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Searching for and Quantifying Nonconvexity Regions of Functions*

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Abstract

Convexity plays a prominent role in a number of areas, but practical considerations often lead to nonconvex functions. We suggest a method for determining regions of convexity and also for assessing the lack of convexity of functions in the other regions. The method relies on a specially constructed decomposition of symmetric matrices. Illustrative examples accompany theoretical results.

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Authors and Affiliations

  1. Chebyshev Laboratory, St. Petersburg State University, St. Petersburg, 199178, Russia

    Youri Davydov

  2. Department of Mathematics & Technion International School, Technion – Israel Institute of Technology, 32000, Haifa, Israel

    Elina Moldavskaya

  3. School of Mathematical and Statistical Sciences, Western University, London, Ontario, N6A 5B7, Canada

    Ričardas Zitikis

Authors
  1. Youri Davydov
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  2. Elina Moldavskaya
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  3. Ričardas Zitikis
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Corresponding author

Correspondence to Ričardas Zitikis.

Additional information

Dedicated to Professor Vygantas Paulauskas, our dear friend, colleague, untiring researcher, and inspiring teacher

*The research has been supported by a grant from the Natural Sciences and Engineering Research Council (NSERC) of Canada and the National Research Organization “Mathematics of Information Technology and Complex Systems” (MITACS) of Canada.

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Davydov, Y., Moldavskaya, E. & Zitikis, R. Searching for and Quantifying Nonconvexity Regions of Functions*. Lith Math J 59, 507–518 (2019). https://doi.org/10.1007/s10986-019-09465-6

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  • DOI: https://doi.org/10.1007/s10986-019-09465-6

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