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The projector onto the Minkowski sum of closed convex sets is generally notequal to the sum of individual projectors. In this work, we provide a completeanswer to the question of characterizing the instances where such an equalityholds. Our results unify and extend the case of linear subspaces andZarantonello's results for projectors onto cones. A detailed analysis in thecase of convex combinations is also carried out. We establish the partial sumproperty for projectors onto convex cones, and we also present various examplesas well as a detailed analysis in the univariate case.

On sums and convex combinations of projectors onto convex sets