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Convexity of the Proximal Average

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Abstract

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.

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Authors and Affiliations

  1. Mathematics, Irving K. Barber School, University of British Columbia Okanagan, Kelowna, British Columbia, V1V 1V7, Canada

    Jennifer A. Johnstone & Valentin R. Koch

  2. Computer Science, Irving K. Barber School, University of British Columbia Okanagan, Kelowna, British Columbia, V1V 1V7, Canada

    Yves Lucet

Authors
  1. Jennifer A. Johnstone
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  2. Valentin R. Koch
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  3. Yves Lucet
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Corresponding author

Correspondence to Yves Lucet.

Additional information

Communicated by F. Zirilli.

The authors would like to thank Dr. Mason Macklem for his carefully reading of the manuscript. Yves Lucet was partially supported by a Discovery grant from the Natural Sciences and Engineering Research Council of Canada. Valentin Koch was partially supported by the Ministry of Advanced Education of the province of British Columbia through a Pacific Century Graduate Scholarship.

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Johnstone, J.A., Koch, V.R. & Lucet, Y. Convexity of the Proximal Average. J Optim Theory Appl 148, 107–124 (2011). https://doi.org/10.1007/s10957-010-9747-5

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