  We report on progress in algorithms for iterative phase retrieval. The theory
of convex optimization is used to develop and to gain insight into counterparts
for the nonconvex problem of phase retrieval. We propose a relaxation of
averaged alternating reflectors and determine the fixed point set of the
related operator in the convex case. A numerical study supports our theoretical
observations and demonstrates the effectiveness of the algorithm compared to
the current state of the art.
