A PARALLEL PROJECTION METHOD BASED ON SEQUENTIAL MOST REMOTE SET IN CONVEX FEASIBILITY PROBLEMS

Recently we proved a theoretical result about the equivalence of the i teration sequence formed by the parallel projection method to find a c ommon point of a finite number of closed convex sets with the iteratio n sequence formed by a sequential projection method with an infinite n umber of closed convex sets. Based on that result we show that for the parallel projection method with variable weights, the weights at each iteration step may be determined by some well-defined criterion; this leads to the determination of those weights at each step by solving a n easy linear programming problem.