  The Method of Alternating Projections (MAP), a classical algorithm for
solving feasibility prob- lems, has recently been intensely studied for
nonconvex sets. However, intrinsically available are only local convergence
results: convergence occurs if the starting point is not too far away from
solutions to avoid getting trapped in certain regions. Instead of taking full
projection steps, it can be advantageous to underrelax, i.e., to move only part
way towards the constraint set, in order to enlarge the regions of convergence.
In this paper, we thus systematically study the Method of Alternating Relaxed
Projections (MARP) for two (possibly nonconvex) sets. Complementing our recent
work on MAP, we es- tablish local linear convergence results for the MARP.
Several examples illustrate our analysis.
