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Convexity of the Proximal Average

Author

Listed:
  • Jennifer A. Johnstone

    (University of British Columbia Okanagan)

  • Valentin R. Koch

    (University of British Columbia Okanagan)

  • Yves Lucet

    (University of British Columbia Okanagan)

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.

Suggested Citation

  • Jennifer A. Johnstone & Valentin R. Koch & Yves Lucet, 2011. "Convexity of the Proximal Average," Journal of Optimization Theory and Applications, Springer, vol. 148(1), pages 107-124, January.
    • Handle: RePEc:spr:joptap:v:148:y:2011:i:1:d:10.1007_s10957-010-9747-5
    DOI: 10.1007/s10957-010-9747-5
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    References listed on IDEAS

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    1. Yves Lucet & Heinz Bauschke & Mike Trienis, 2009. "The piecewise linear-quadratic model for computational convex analysis," Computational Optimization and Applications, Springer, vol. 43(1), pages 95-118, May.
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    Cited by:

    1. Bryan Gardiner & Khan Jakee & Yves Lucet, 2014. "Computing the partial conjugate of convex piecewise linear-quadratic bivariate functions," Computational Optimization and Applications, Springer, vol. 58(1), pages 249-272, May.

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