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In this tutorial paper, we consider the problem of minimizing the rank of a matrix over a convex set. The rank minimization problem (RMP) arises in diverse areas such as control, system identification, statistics and signal processing, and is known to be computationally NP-hard. We give an overview of the problem, its interpretations, applications, and solution methods. In particular, we focus on how convex optimization can be used to develop heuristic methods for this problem.
Fazel et al. (Thu,) studied this question.