Nk 8.27 Problems with minimum distance constraints. We consider a problem with variables 21, ... , XN Rk. The objective, fo(21, ..., XN), is convex, and the constraints fi(x1,...,IN) Dmin, i #j, i, j = 1,..., N. In general, this is a hard nonconvex problem. Following the approach taken in floorplanning, we can form a convex restriction of the problem, i.e., a problem which is convex, but has a smaller feasible set. (Solving the restricted problem is therefore easy, and any solution is guaranteed to be feasible for the nonconvex problem.) Let aij ERK, for i Dmin, i Dmin, i #j, i, j = 1,..., N. In general, this is a hard nonconvex problem. Following the approach taken in floorplanning, we can form a convex restriction of the problem, i.e., a problem which is convex, but has a smaller feasible set. (Solving the restricted problem is therefore easy, and any solution is guaranteed to be feasible for the nonconvex problem.) Let aij ERK, for i Dmin, i