Generalized projections onto convex sets

Authors:
O. P. Ferreira;S. Z. Németh
Affiliations:
IME/UFG, Goiânia, Brazil 74001-970;School of Mathematics, The University of Birmingham, Edgbaston, Birmingham, United Kingdom B15 2TT
Venue:
Journal of Global Optimization
Year:
2012

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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.