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The NC-proximal average for multiple functions

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Abstract

The NC-proximal average is a parametrized function used to continuously transform one proper, lsc, prox-bounded function into another. Until now it has been defined for two functions. The purpose of this article is to redefine it so that any finite number of functions may be used. The layout generally follows that of Hare (SIAM J Optim 20(2):650–666, 2009), extending those results to the more general case and in some instances giving alternate proofs by using techniques developed after the publication of that paper. We conclude with an example examining the discontinuity of the minimizers of the NC-proximal average.

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Authors and Affiliations

  1. Mathematics, University of British Columbia, 3333 University Way, Kelowna, Canada

    W. Hare & C. Planiden

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  1. W. Hare
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  2. C. Planiden
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Correspondence to W. Hare.

Additional information

Research by these authors was supported by UBC UGF and by NSERC of Canada.

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Hare, W., Planiden, C. The NC-proximal average for multiple functions. Optim Lett 8, 849–860 (2014). https://doi.org/10.1007/s11590-013-0641-6

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  • DOI: https://doi.org/10.1007/s11590-013-0641-6

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