TY - JOUR
T1 - Distributed Design for Nuclear Norm Minimization of Linear Matrix Equations with Constraints
AU - Li, Weijian
AU - Zeng, Xianlin
AU - Hong, Yiguang
AU - Ji, Haibo
N1 - Publisher Copyright:
© 1963-2012 IEEE.
PY - 2021/2
Y1 - 2021/2
N2 - This article aims at a distributed design to minimize the nuclear norm (the sum of all singular values) under linear equality constraints over a multiagent network. The problem is reformulated as a distributed trace norm minimization problem by introducing substitutional variables. A distributed projected primal-dual algorithm is proposed for the reformulation. It is shown that the algorithm converges to an optimal solution with a rate of \mathcal O(1/t). Numerical simulations on three classical problems, including linear matrix equality constraints, cardinality minimization, and low-rank matrix completion, are carried out for illustration.
AB - This article aims at a distributed design to minimize the nuclear norm (the sum of all singular values) under linear equality constraints over a multiagent network. The problem is reformulated as a distributed trace norm minimization problem by introducing substitutional variables. A distributed projected primal-dual algorithm is proposed for the reformulation. It is shown that the algorithm converges to an optimal solution with a rate of \mathcal O(1/t). Numerical simulations on three classical problems, including linear matrix equality constraints, cardinality minimization, and low-rank matrix completion, are carried out for illustration.
KW - Distributed matrix computation
KW - distributed optimization
KW - linear equality constraints
KW - nuclear norm minimization
UR - http://www.scopus.com/inward/record.url?scp=85100395602&partnerID=8YFLogxK
U2 - 10.1109/TAC.2020.2981930
DO - 10.1109/TAC.2020.2981930
M3 - Article
AN - SCOPUS:85100395602
SN - 0018-9286
VL - 66
SP - 745
EP - 752
JO - IEEE Transactions on Automatic Control
JF - IEEE Transactions on Automatic Control
IS - 2
M1 - 9042312
ER -