Low-rank spectral optimization

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 solving a certain constrained eigenvalue optimization problem that corresponds to the gauge dual. Numerical examples on a range of problems illustrate the effectiveness of the approach.



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