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Phase retrieval can be expressed as one non-convex constrained optimizationproblem to identify one phase minimizer in the primal space. Many iterativetransform techniques have been proposed to identify the minimizer, e.g.,relaxed averaged alternating reflections(RAAR) algorithms. RAAR algorithm isone alternating direction method of multipliers(ADMM) with one penaltyparameter. Pairing with multipliers (dual vectors), phase vectors are lifted tohigher dimensional vectors, RAAR algorithms actually is one continuationalgorithm, which searches for local Nash equilibria in a primal-dual space. Thedual iteration approximates one gradient ascent flow, which drives thecorresponding local minimizers in a positive-definite Hessian region. Thepenalty parameter, which is the reciprocal of the RAAR parameter, plays a roleof altering the size of the attractor basin for each stationary point. Underproper penalty parameters, the RAAR avoids the stagnation of thesecorresponding local minimizers in the primal space and thus screens out manystationary points corresponding to non-local minimizers.

Local saddle structure in relaxed averaged alternating reflections Algorithms on phase retrieval