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.
Original language | English |
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Pages (from-to) | 831-842 |
Number of pages | 12 |
Journal | Journal of Global Optimization |
Volume | 52 |
Issue number | 4 |
DOIs | |
Publication status | Published - 1 Apr 2012 |