Various applications in signal processing and machine learning give rise to highly structured spectral optimization problems characterized by low-rank solutions. Two important examples that motivate this work are optimization problems from phase retrieval and from blind deconvolution, which are designed to yield rank-1 solutions. An algorithm is described based on solving a certain constrained eigenvalue optimization problem that corresponds to the gauge dual. Numerical examples on a range of problems illustrate the e ffectiveness of the approach.
The implementation is here: https://www.math.ucdavis.edu/~mpf/2015-spectral-low-rank.html
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