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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.

- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E93-A No.2 pp.456-466

- Publication Date
- 2010/02/01

- Publicized

- Online ISSN
- 1745-1337

- DOI
- 10.1587/transfun.E93.A.456

- Type of Manuscript
- PAPER

- Category
- Digital Signal Processing

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Masahiro YUKAWA, Konstantinos SLAVAKIS, Isao YAMADA, "Multi-Domain Adaptive Learning Based on Feasibility Splitting and Adaptive Projected Subgradient Method" in IEICE TRANSACTIONS on Fundamentals,
vol. E93-A, no. 2, pp. 456-466, February 2010, doi: 10.1587/transfun.E93.A.456.

Abstract: 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.

URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E93.A.456/_p

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@ARTICLE{e93-a_2_456,

author={Masahiro YUKAWA, Konstantinos SLAVAKIS, Isao YAMADA, },

journal={IEICE TRANSACTIONS on Fundamentals},

title={Multi-Domain Adaptive Learning Based on Feasibility Splitting and Adaptive Projected Subgradient Method},

year={2010},

volume={E93-A},

number={2},

pages={456-466},

abstract={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.},

keywords={},

doi={10.1587/transfun.E93.A.456},

ISSN={1745-1337},

month={February},}

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TY - JOUR

TI - Multi-Domain Adaptive Learning Based on Feasibility Splitting and Adaptive Projected Subgradient Method

T2 - IEICE TRANSACTIONS on Fundamentals

SP - 456

EP - 466

AU - Masahiro YUKAWA

AU - Konstantinos SLAVAKIS

AU - Isao YAMADA

PY - 2010

DO - 10.1587/transfun.E93.A.456

JO - IEICE TRANSACTIONS on Fundamentals

SN - 1745-1337

VL - E93-A

IS - 2

JA - IEICE TRANSACTIONS on Fundamentals

Y1 - February 2010

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.

ER -