Algorithms for Rank Minimization of Structured Matrices

Maryam Fazel
University of Washington

Rank minimization problems in which the matrix variable has linear structure, such as
block-Hankel, Toeplitz, or moment structure, arise in many applications. Examples in systems theory and statistical signal processing include
input-output linear system identification, minimal stochastic realization, structured total least squares, and shape from moments estimation. We present efficient algorithms for minimizing the nuclear norm for such structured matrices (including an Alternating Directions Method and a Dual Gradient Projection method) and show their numerical performance on random instances as
well as some benchmark system identification problems. This is joint work with
Ting Kei Pong, Defeng Sun, and Paul Tseng.

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