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Journal of Global Optimization

, Volume 52, Issue 4, pp 831–842 | Cite as

Generalized projections onto convex sets

  • O. P. Ferreira
  • S. Z. Németh
Article

Abstract

This paper introduces the notion of projection onto a closed convex set associated with a convex function. Several properties of the usual projection are extended to this setting. In particular, a generalization of Moreau’s decomposition theorem about projecting onto closed convex cones is given. Several examples of distances and the corresponding generalized projections associated to particular convex functions are presented.

Keywords

Projection Convex set Convex cone Convex function 

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Copyright information

© Springer Science+Business Media, LLC. 2011

Authors and Affiliations

  1. 1.IME/UFGGoiâniaBrazil
  2. 2.School of MathematicsThe University of BirminghamEdgbaston, BirminghamUnited Kingdom

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