Convergence of string-averaging projection schemes for inconsistent convex feasibility problems

We study iterative projection algorithms for the convex feasibility problem of finding a point in the intersection of finitely many nonempty, closed and convex subsets in the Euclidean space. We propose (without proof) an algorithmic scheme which generalizes both the string-averaging algorithm and the block-iterative projections (BIP) method with fixed blocks and prove convergence of the string-averaging method in the inconsistent case by translating it into a fully sequential algorithm in the product space.


Optimization Methods and Software, Vol. 18 (2003), pp. 543-554.