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Self-Dual Smooth Approximations of Convex Functions via the Proximal Average

In: Fixed-Point Algorithms for Inverse Problems in Science and Engineering

Author

Listed:
  • Heinz H. Bauschke

    (University of British Columbia)

  • Sarah M. Moffat
  • Xianfu Wang

Abstract

The proximal average of two convex functions has proven to be a useful tool in convex analysis. In this note, we express the Goebel self-dual smoothing operator in terms of the proximal average, which allows us to give a different proof of self duality. We also provide a novel self-dual smoothing operator. Both operators are illustrated by smoothing the norm.

Suggested Citation

  • Heinz H. Bauschke & Sarah M. Moffat & Xianfu Wang, 2011. "Self-Dual Smooth Approximations of Convex Functions via the Proximal Average," Springer Optimization and Its Applications, in: Heinz H. Bauschke & Regina S. Burachik & Patrick L. Combettes & Veit Elser & D. Russell Luke & Henry (ed.), Fixed-Point Algorithms for Inverse Problems in Science and Engineering, chapter 0, pages 23-32, Springer.
    • Handle: RePEc:spr:spochp:978-1-4419-9569-8_2
    DOI: 10.1007/978-1-4419-9569-8_2
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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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