Convergence of weighted averages of relaxed projections

TL;DR

This paper investigates the convergence properties of algorithms based on weighted averages of relaxed projections for solving convex feasibility problems, extending previous results with new methods and illustrative examples.

Contribution

It introduces new methods that generalize existing convergence results for weighted averages of relaxed projections in convex feasibility algorithms.

Findings

Established convergence of the generalized algorithms.

Provided examples demonstrating the new methods.

Extended prior theoretical results.

Abstract

The convergence of the algorithm for solving convex feasibility problem is studied by the method of sequential averaged and relaxed projections. Some results of H. H. Bauschke and J. M. Borwein are generalized by introducing new methods. Examples illustrating these generalizations are given.