Finding the projection of a point onto the intersection of convex sets via projections onto half-spaces

We present a modification of Dykstra’s algorithm which allows us to avoid projections onto general convex sets. Instead, we calculate projections onto either a halfspace or onto the intersection of two halfspaces. Convergence of the algorithm is established and special choices of the halfspaces are proposed. The option to project onto halfspaces instead of general convex sets makes the algorithm more practical. The fact that the halfspaces