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Lithuanian Mathematical Journal

, Volume 59, Issue 4, pp 507–518 | Cite as

Searching for and Quantifying Nonconvexity Regions of Functions*

  • Youri Davydov
  • Elina Moldavskaya
  • Ričardas ZitikisEmail author
Article
  • 11 Downloads

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.

Keywords

convex analysis nonconvexity penalty function Hessian Weyl inequality risk assessment 

MSC

15B57 26B25 52A41 91G80 

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Notes

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Youri Davydov
    • 1
  • Elina Moldavskaya
    • 2
  • Ričardas Zitikis
    • 3
    Email author
  1. 1.Chebyshev Laboratory, St. Petersburg State UniversitySt. PetersburgRussia
  2. 2.Department of Mathematics & Technion International School, Technion – Israel Institute of TechnologyHaifaIsrael
  3. 3.School of Mathematical and Statistical SciencesWestern UniversityLondonCanada

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