Adaptive projected subgradient method and set theoretic adaptive filtering with multiple convex constraints
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 propose...
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| Vydané v: | 2004 38th Asilomar Conference on Signals, Systems and Computers Ročník 1; s. 960 - 964 Vol.1 |
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| Hlavní autori: | , , , |
| Médium: | Konferenčný príspevok.. |
| Jazyk: | English |
| Vydavateľské údaje: |
Piscataway NJ
IEEE
2004
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| ISBN: | 0780386221, 9780780386228 |
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| 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. |
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| AbstractList | 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. |
| Author | Yamada, I. Ogura, N. Yukawa, M. Slavakis, K. |
| Author_xml | – sequence: 1 givenname: K. surname: Slavakis fullname: Slavakis, K. organization: Dept. of Commun. & Integrated Syst., Tokyo Inst. of Technol., Japan – sequence: 2 givenname: I. surname: Yamada fullname: Yamada, I. organization: Dept. of Commun. & Integrated Syst., Tokyo Inst. of Technol., Japan – sequence: 3 givenname: N. surname: Ogura fullname: Ogura, N. – sequence: 4 givenname: M. surname: Yukawa fullname: Yukawa, M. |
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| Keywords | Performance evaluation Parallel algorithm Convex set Adaptive algorithm Maximin problem Stereophony Algorithmics Adaptive filtering Continuous function Mapping Acoustic signal processing Adaptive method Minimax method Unification Numerical simulation Set theory Hilbert space Convex function Asymptotic approximation Least mean squares methods Fixed point |
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| PublicationTitle | 2004 38th Asilomar Conference on Signals, Systems and Computers |
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| SubjectTerms | Adaptive filters Applied sciences Constraint theory Convergence Detection, estimation, filtering, equalization, prediction Echo cancellers Exact sciences and technology Filtering algorithms Hilbert space Information, signal and communications theory Miscellaneous Projection algorithms Resonance light scattering Signal and communications theory Signal processing Signal processing algorithms Signal, noise Telecommunications and information theory Working environment noise |
| Title | Adaptive projected subgradient method and set theoretic adaptive filtering with multiple convex constraints |
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