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.
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This work was done while the first author was visiting the second author at the School of Mathematics in The University of Birmingham, during the period of January 2010 to July 2010.
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Ferreira, O.P., Németh, S.Z. Generalized projections onto convex sets. J Glob Optim 52, 831–842 (2012). https://doi.org/10.1007/s10898-011-9714-1
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DOI: https://doi.org/10.1007/s10898-011-9714-1