A parallel projection method based on sequential most remote set in convex feasibility problems (Q1907078)

The parallel projection method with variable weights to find a common point of a finite number of closed convex sets in the Hilbert space is equivalent to an iteration sequence formed by a sequential projection method in another Hilbert space, involving a corresponding sequence, a closed linear subspace and infinite number of suitable closed convex sets, where each set is determined by the choice of the weights of the initial projection procedure to find a common point, and leads to determination of those weights by solving a certain linear programming problem.