Dykstra’s algorithm with strategies for projecting onto certain polyhedral cones

Abstract

We consider Dykstra’s alternating projection method when it is used to find the projection onto polyhedral cones of the form {x Î H : á vi, xñ £ 0} where H is a real Hilbert space and á vi, vjñ > 0, i, j = 1, ..., n. Based on some properties of the projection, we propose strategies with the aim to reduce the number of cycles and the execution time. These strategies consist in previous discarding and arrangement, and in projecting cyclically onto the intersection of two halfspaces. Encouraging preliminary numerical results with cut semimetrics as vectors vi are presented.