TY - GEN
T1 - An ADMM algorithm for matrix completion of partially known state covariances
AU - Lin, Fu
AU - Jovanović, Mihailo R.
AU - Georgiou, Tryphon T.
PY - 2013
Y1 - 2013
N2 - We study the inverse problem of reproducing partially known second-order statistics of a linear time invariant system by the least number of possible input disturbance channels. This can be formulated as a rank minimization problem, and for its solution, we employ a convex relaxation based on the nuclear norm. The resulting optimization problem can be cast as a semi-definite program and solved efficiently using generalpurpose solvers for small- And medium-size problems. In this paper, we focus on issues and techniques that are pertinent to large-scale systems. We bring in a re-parameterization which transforms the problem into a form suitable for the alternating direction method of multipliers. Furthermore, we show that each iteration of this algorithm amounts to solving a system of linear equations, an eigenvalue decomposition, and a singular value thresholding. An illustrative example is provided to demonstrate the effectiveness of the developed approach.
AB - We study the inverse problem of reproducing partially known second-order statistics of a linear time invariant system by the least number of possible input disturbance channels. This can be formulated as a rank minimization problem, and for its solution, we employ a convex relaxation based on the nuclear norm. The resulting optimization problem can be cast as a semi-definite program and solved efficiently using generalpurpose solvers for small- And medium-size problems. In this paper, we focus on issues and techniques that are pertinent to large-scale systems. We bring in a re-parameterization which transforms the problem into a form suitable for the alternating direction method of multipliers. Furthermore, we show that each iteration of this algorithm amounts to solving a system of linear equations, an eigenvalue decomposition, and a singular value thresholding. An illustrative example is provided to demonstrate the effectiveness of the developed approach.
KW - Alternating direction method of multipliers
KW - Convex optimization
KW - Low-rank approximation
KW - Nuclear norm regularization
KW - Singular value thresholding
KW - State covariances
KW - Structured matrix completion problems
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U2 - 10.1109/CDC.2013.6760124
DO - 10.1109/CDC.2013.6760124
M3 - Conference contribution
AN - SCOPUS:84902353907
SN - 9781467357173
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 1684
EP - 1689
BT - 2013 IEEE 52nd Annual Conference on Decision and Control, CDC 2013
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 52nd IEEE Conference on Decision and Control, CDC 2013
Y2 - 10 December 2013 through 13 December 2013
ER -