Number Of Closed Convex Sets Research Articles

Finding projections onto the intersection of convex sets in Hilbert spaces. II

We present a parallel iterative algorithm to find the shortest distance projection of a given point onto the intersection of a finite number of closed convex sets in a real Hilbert space; the number of sets used at each iteration step, corresponding to the number of available processors, may be smaller than the total number of sets. The relaxation coefficient at each iteraction step is determined by a geometric condition in an associated Hilbert space, while for the weights mild conditions are given to assure norm convergence of the resulting sequence. These mild conditions leave enough flexibility to determine the weights more specifically in order to improve the speed of convergence.