2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/141858Iterative algorithms with feedback are amongst 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.8 pages, 4 figures, revtexOpticsOptimization and Controltext