The NC-proximal average for multiple functions

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Optimization Letters, ISSN: 1862-4472, Vol: 8, Issue: 3, Page: 849-860

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Planiden, Chayne; Hare, Warren L
Springer Nature
Mathematics; Engineering; Science and Technology Studies
article description
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. © 2013 Springer-Verlag Berlin Heidelberg.