Multi-domain adaptive learning based on feasibility splitting and adaptive projected subgradient method

Masahiro Yukawa, Konstantinos Slavakis, Isao Yamada

Research output: Contribution to journalArticlepeer-review

19 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)456-466
Number of pages11
JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Issue number2
Publication statusPublished - 2010 Feb
Externally publishedYes


  • Adaptive algorithm
  • Convex feasibility problem
  • Convex projection
  • Projected gradient method

ASJC Scopus subject areas

  • Signal Processing
  • Computer Graphics and Computer-Aided Design
  • Electrical and Electronic Engineering
  • Applied Mathematics


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