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.
|Number of pages||12|
|Journal||Journal of Global Optimization|
|Publication status||Published - 1 Apr 2012|