TY - JOUR
T1 - Adaptive projected subgradient method and set theoretic adaptive filtering with multiple convex constraints
AU - Slavakis, Konstantinos
AU - Yamada, Isao
AU - Ogura, Nobuhiko
AU - Yukawa, Masahiro
PY - 2004/12/1
Y1 - 2004/12/1
N2 - This paper presents an algorithmic solution, the Adaptive Projected Subgradient Method, to the problem of asymptotically minimizing a certain sequence of nonnegative continuous convex functions over the fixed point set of strongly attracting nonexpansive mappings in a real Hilbert space. The proposed method provides with a strongly convergent, asymptotically optimal point sequence as well as with a characterization of the limiting point. As a side effect, the method allows the asymptotic minimization over the nonempty intersection of a finite number of closed convex sets. Thus, new directions for set theoretic adaptive filtering algorithms are revealed whenever the estimandum (system to be identified) is known to satisfy a number of convex constraints. This leads to a unification of a wide range of set theoretic adaptive filtering schemes such as NLMS, Projected or Constrained NLMS, APA, Adaptive Parallel Subgradient Projection Algorithm, Adaptive Parallel Min-Max Projection Algorithm as well as their embedded constraint versions. Numerical results demonstrate the effectiveness of the proposed method to the problem of stereophonic acoustic echo cancellation.
AB - This paper presents an algorithmic solution, the Adaptive Projected Subgradient Method, to the problem of asymptotically minimizing a certain sequence of nonnegative continuous convex functions over the fixed point set of strongly attracting nonexpansive mappings in a real Hilbert space. The proposed method provides with a strongly convergent, asymptotically optimal point sequence as well as with a characterization of the limiting point. As a side effect, the method allows the asymptotic minimization over the nonempty intersection of a finite number of closed convex sets. Thus, new directions for set theoretic adaptive filtering algorithms are revealed whenever the estimandum (system to be identified) is known to satisfy a number of convex constraints. This leads to a unification of a wide range of set theoretic adaptive filtering schemes such as NLMS, Projected or Constrained NLMS, APA, Adaptive Parallel Subgradient Projection Algorithm, Adaptive Parallel Min-Max Projection Algorithm as well as their embedded constraint versions. Numerical results demonstrate the effectiveness of the proposed method to the problem of stereophonic acoustic echo cancellation.
UR - http://www.scopus.com/inward/record.url?scp=21644444200&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=21644444200&partnerID=8YFLogxK
M3 - Conference article
AN - SCOPUS:21644444200
VL - 1
SP - 960
EP - 964
JO - Conference Record of the Asilomar Conference on Signals, Systems and Computers
JF - Conference Record of the Asilomar Conference on Signals, Systems and Computers
SN - 1058-6393
T2 - Conference Record of the Thirty-Eighth Asilomar Conference on Signals, Systems and Computers
Y2 - 7 November 2004 through 10 November 2004
ER -