Journal of Optimization Theory and Applications

, Volume 148, Issue 1, pp 107–124 | Cite as

Convexity of the Proximal Average

  • Jennifer A. Johnstone
  • Valentin R. Koch
  • Yves LucetEmail author


We complete the study of the convexity of the proximal average by proving it is convex as a function of each of its parameters separately, but not jointly convex as a function of any two of its parameters. We present an interpolation-based plotting algorithm that takes advantage of the partial convexity of the proximal average, and improves the plotting time by a factor of 100, while reducing picture sizes by a factor of 10.


Convex analysis Proximal average Convexity Interpolation 


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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Jennifer A. Johnstone
    • 1
  • Valentin R. Koch
    • 1
  • Yves Lucet
    • 2
    Email author
  1. 1.Mathematics, Irving K. Barber SchoolUniversity of British Columbia OkanaganKelownaCanada
  2. 2.Computer Science, Irving K. Barber SchoolUniversity of British Columbia OkanaganKelownaCanada

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