Optimization Online


The nonsmooth landscape of phase retrieval

Damek Davis(dsd95***at***cornell.edu)
Dmitriy Drusvyatskiy(ddrusv***at***uw.edu)
Courtney Paquette(yumiko88***at***uw.edu)

Abstract: We consider a popular nonsmooth formulation of the real phase retrieval problem. We show that under standard statistical assumptions, a simple subgradient method converges linearly when initialized within a constant relative distance of an optimal solution. Seeking to understand the distribution of the stationary points of the problem, we complete the paper by proving that as the number of Gaussian measurements increases, the stationary points converge to a codimension two set, at a controlled rate. Experiments on image recovery problems illustrate the developed algorithm and theory.

Keywords: Phase retrieval, stationary points, subdifferential, variational principle, subgradient method, spectral functions, eigenvalues

Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization )


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Entry Submitted: 11/09/2017
Entry Accepted: 11/09/2017
Entry Last Modified: 11/09/2017

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