TY - JOUR
T1 - Multi-domain adaptive learning based on feasibility splitting and adaptive projected subgradient method
AU - Yukawa, Masahiro
AU - Slavakis, Konstantinos
AU - Yamada, Isao
PY - 2010/2
Y1 - 2010/2
N2 - We propose the multi-domain adaptive learning that enables us to find a point meeting possibly time-varying specifications simultaneously in multiple domains, e.g. space, time, frequency, etc. The novel concept is based on the idea of feasibility splitting - dealing with feasibility in each individual domain. We show that the adaptive projected subgradient method (Yamada, 2003) realizes the multi-domain adaptive learning by employing (i) a projected gradient operator with respect to a 'fixed' proximity function reflecting the time-invariant specifications and (ii) a subgradient projection with respect to 'time-varying' objective functions reflecting the time-varying specifications. The resulting algorithm is suitable for real-time implementation, because it requires no more than metric projections onto closed convex sets each of which accommodates the specification in each domain. A convergence analysis and numerical examples are presented.
AB - We propose the multi-domain adaptive learning that enables us to find a point meeting possibly time-varying specifications simultaneously in multiple domains, e.g. space, time, frequency, etc. The novel concept is based on the idea of feasibility splitting - dealing with feasibility in each individual domain. We show that the adaptive projected subgradient method (Yamada, 2003) realizes the multi-domain adaptive learning by employing (i) a projected gradient operator with respect to a 'fixed' proximity function reflecting the time-invariant specifications and (ii) a subgradient projection with respect to 'time-varying' objective functions reflecting the time-varying specifications. The resulting algorithm is suitable for real-time implementation, because it requires no more than metric projections onto closed convex sets each of which accommodates the specification in each domain. A convergence analysis and numerical examples are presented.
KW - Adaptive algorithm
KW - Convex feasibility problem
KW - Convex projection
KW - Projected gradient method
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U2 - 10.1587/transfun.E93.A.456
DO - 10.1587/transfun.E93.A.456
M3 - Article
AN - SCOPUS:77950789961
SN - 0916-8508
VL - E93-A
SP - 456
EP - 466
JO - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
JF - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
IS - 2
ER -