Aspects of the Projector on Prox-Regular Sets.

This paper deals with results about projectors on the important class of closed, prox-regular sets in ℝn. These sets, which include all closed convex sets but also many nonconvex sets, have the property that their associated projection mappings are very well behaved, being locally single-valued and continuous among other good properties. We give elementary proofs of these properties of the projector, and for the case in which the projection is made onto a perturbed set we show that under suitable conditions the projector is jointly continuous in the perturbation variable and the variable expressing the point that is projected. We briefly describe an application to the extension of a normal-map construction from variational inequalities posed over polyhedral convex sets to variational conditions posed over sets that satisfy prox-regularity. [ABSTRACT FROM AUTHOR]