Abstract — We present an algorithm to solve a structured low rank matrix optimization problem based on the nuclear norm. We represent the desired structure by a linear map, termed mutation, that we characterize and use in our algorithm. Contrary to alternative techniques for structured low rank matrices, the algorithm is SVD-free, which leads to improved scalability. The idea relies on restating the nuclear norm via an equivalent variational reformulation involving explicit matrix factors. We detail the procedure for a general class of problems and then discuss its application to linear system identification with input and output missing data. A direct comparison between alternative approaches highlights the advantage of SVD-free computations. I
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