Skip to main content
placeholder image

The NC-proximal average for multiple functions

Journal Article


Download full-text (Open Access)

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 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.

Publication Date


  • 2014

Geographic Focus


Citation


  • Planiden, C. & Hare, W. L. (2014). The NC-proximal average for multiple functions. Optimization Letters, 8 (3), 849-860.

Scopus Eid


  • 2-s2.0-84894619649

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=2116&context=eispapers1

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers1/1114

Number Of Pages


  • 11

Start Page


  • 849

End Page


  • 860

Volume


  • 8

Issue


  • 3

Place Of Publication


  • Germany

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 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.

Publication Date


  • 2014

Geographic Focus


Citation


  • Planiden, C. & Hare, W. L. (2014). The NC-proximal average for multiple functions. Optimization Letters, 8 (3), 849-860.

Scopus Eid


  • 2-s2.0-84894619649

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=2116&context=eispapers1

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers1/1114

Number Of Pages


  • 11

Start Page


  • 849

End Page


  • 860

Volume


  • 8

Issue


  • 3

Place Of Publication


  • Germany