A parallel projection method based on sequential most remote set in convex feasibility problems

摘要

Recently we proved a theoretical result about the equivalence of the iteration sequence formed by the parallel projection method to find a common point of a finite number of closed convex sets with the iteration sequence formed by a sequential projection method with an infinite number 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 an easy linear programming problem.