Rank Minimization and Applications in System Theory
Abstract¶
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.
Summary¶
Surveys matrix rank minimization, its applications in system theory and related fields, and convex-optimization heuristics for handling an NP-hard objective. The paper provides a tutorial bridge from rank-constrained control and identification problems to nuclear-norm, trace, and related convex relaxations.
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