Adaptive projected subgradient method and set theoretic adaptive filtering with multiple convex constraints

Konstantinos Slavakis, Isao Yamada, Nobuhiko Ogura, Masahiro Yukawa

Research output: Chapter in Book/Report/Conference proceedingConference contribution

5 Citations (Scopus)

Abstract

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.

Original languageEnglish
Title of host publicationConference Record - Asilomar Conference on Signals, Systems and Computers
EditorsM.B. Matthews
Pages960-964
Number of pages5
Volume1
Publication statusPublished - 2004
Externally publishedYes
EventConference Record of the Thirty-Eighth Asilomar Conference on Signals, Systems and Computers - Pacific Grove, CA, United States
Duration: 2004 Nov 72004 Nov 10

Other

OtherConference Record of the Thirty-Eighth Asilomar Conference on Signals, Systems and Computers
CountryUnited States
CityPacific Grove, CA
Period04/11/704/11/10

Fingerprint

Adaptive filtering
Echo suppression
Hilbert spaces
Adaptive algorithms
Acoustics

ASJC Scopus subject areas

  • Engineering(all)

Cite this

Slavakis, K., Yamada, I., Ogura, N., & Yukawa, M. (2004). Adaptive projected subgradient method and set theoretic adaptive filtering with multiple convex constraints. In M. B. Matthews (Ed.), Conference Record - Asilomar Conference on Signals, Systems and Computers (Vol. 1, pp. 960-964)

Adaptive projected subgradient method and set theoretic adaptive filtering with multiple convex constraints. / Slavakis, Konstantinos; Yamada, Isao; Ogura, Nobuhiko; Yukawa, Masahiro.

Conference Record - Asilomar Conference on Signals, Systems and Computers. ed. / M.B. Matthews. Vol. 1 2004. p. 960-964.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Slavakis, K, Yamada, I, Ogura, N & Yukawa, M 2004, Adaptive projected subgradient method and set theoretic adaptive filtering with multiple convex constraints. in MB Matthews (ed.), Conference Record - Asilomar Conference on Signals, Systems and Computers. vol. 1, pp. 960-964, Conference Record of the Thirty-Eighth Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, United States, 04/11/7.
Slavakis K, Yamada I, Ogura N, Yukawa M. Adaptive projected subgradient method and set theoretic adaptive filtering with multiple convex constraints. In Matthews MB, editor, Conference Record - Asilomar Conference on Signals, Systems and Computers. Vol. 1. 2004. p. 960-964
Slavakis, Konstantinos ; Yamada, Isao ; Ogura, Nobuhiko ; Yukawa, Masahiro. / Adaptive projected subgradient method and set theoretic adaptive filtering with multiple convex constraints. Conference Record - Asilomar Conference on Signals, Systems and Computers. editor / M.B. Matthews. Vol. 1 2004. pp. 960-964
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