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In this paper we present a new iterative projection method for finding theclosest point in the intersection of convex sets to any arbitrary point in aHilbert space. This method, termed AAMR for averaged alternating modifiedreflections, can be viewed as an adequate modification of the Douglas--Rachfordmethod that yields a solution to the best approximation problem. Under aconstraint qualification at the point of interest, we show strong convergenceof the method. In fact, the so-called strong CHIP fully characterizes theconvergence of the AAMR method for every point in the space. We report somepromising numerical experiments where we compare the performance of AAMRagainst other projection methods for finding the closest point in theintersection of pairs of finite dimensional subspaces.

A new projection method for finding the closest point in the intersection of convex sets