Phase retrieval and saddle-point optimization.

Iterative algorithms with feedback are among the most powerful and versatile optimization methods for phase retrieval. Among these, the hybrid input-output algorithm has demonstrated practical solutions to giga-element nonlinear phase retrieval problems, escaping local minima and producing images at resolutions beyond the capabilities of lens-based optical methods. Here the input-output iteration is improved by a lower-dimensional subspace saddle-point optimization.