There have been some algorithms for finding the projection from a given point onto a convex set. This problem seems to be quit easy because of the convexity of the set. However, in the case of finding the minimum distance from an interior point to the complement of a convex set, the convexity no longer exists. In this case, the solution set (the set of all projections) is a set in general.
My question is: Is there any algorithm for finding the minimum distance (and/or finding a point in the set of projections) from a point to a reverse convex set?
If the nom is polyhedral $(l_1, l_\infty)$ it can be computed with a finite number of linear program (the problem is polynomial in the $l_1$ case)