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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Bibliographic Details
Published in:2004 38th Asilomar Conference on Signals, Systems and Computers Vol. 1; pp. 960 - 964 Vol.1
Main Authors: Slavakis, K., Yamada, I., Ogura, N., Yukawa, M.
Format: Conference Proceeding
Language:English
Published: Piscataway NJ IEEE 2004
Subjects:
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
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
ISBN:0780386221, 9780780386228
Online Access:Get full text
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Summary: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.
ISBN:0780386221
9780780386228
DOI:10.1109/ACSSC.2004.1399281