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均衡問題に関する逐次アルゴリズムとパワーコントロールへの応用

Research Project

Project/Area Number 07J01979
Research Category

Grant-in-Aid for JSPS Fellows

Allocation TypeSingle-year Grants
Section国内
Research Field Sensitivity informatics/Soft computing
Research InstitutionKyushu Institute of Technology (2008)
Tokyo Institute of Technology (2007)

Principal Investigator

飯塚 秀明  Kyushu Institute of Technology, ネットワークデザイン研究センター, 准教授

Project Period (FY) 2007 – 2008
Project Status Completed (Fiscal Year 2008)
Budget Amount *help
¥2,200,000 (Direct Cost: ¥2,200,000)
Fiscal Year 2008: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2007: ¥1,100,000 (Direct Cost: ¥1,100,000)
Keywords電力制御 / 逐次アルゴリズム / 収束 / ナッシュ均衡問題 / 変分不等式問題 / 非拡大写像 / 不動点 / アルゴリズム
Research Abstract

既存の電力制御問題では、基地局から遠く離れたユーザーは最低限のサービスさえ得られる保証がない。その問題点を解消するために、平成19年度では、「すべてのユーザーが十分なサービスを得ることができる電力制御問題」の提案をした。既存の電力制御問題の戦略集合にすべてのユーザーが最低限の品質を得られるような新たな条件を加えることで問題を導入することができている。しかしながら、新たな条件を与えたために、この問題の解明は大変困難なものになった。平成19年度では、この電力制御問題を解くための逐次アルゴリズムと問題の解への収束性について提案している。しかしながら、このアルゴリズムは「平均手法」を利用しているため、計算時間量が大変多くなり、実用性の観点から見て理想的とは言えない。
平成20年度では、平均手法の問題点を解消することができるアルゴリズムを提案することができた。提案アルゴリズムは「平均手法」の代わりに「凸結合」を利用しており、計算量を大幅に減少させることに成功している。提案アルゴリズムに関する解への収束性についても数学的に証明することができている。これらの結果は応用数学や数理工学の観点から見ても新しくまた画期的でもある。この結果やそれに至るまでのアイデアは、「ロバスト制御」や「ネットワーク制御」といった実践的な工学の諸問題を解決する上で本質的な部分を占めており、今後の研究の基礎部分を構築することができる。

Report

(2 results)
  • 2008 Annual Research Report
  • 2007 Annual Research Report
  • Research Products

    (22 results)

All 2009 2008 2007 Other

All Journal Article (11 results) (of which Peer Reviewed: 9 results) Presentation (10 results) Remarks (1 results)

  • [Journal Article] An ergodic algorithm for the power-control games for CDMA data networks2009

    • Author(s)
      Hideaki IIDUKA, Isao YAMADA
    • Journal Title

      Journal of Mathematical Modelling and Algorithms 8

      Pages: 1-18

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A use of conjugate gradient direction for the convex optimization problem over the fixed point set of a nonexpansive mapping2009

    • Author(s)
      Hideaki IIDUKA, Isao YAMADA
    • Journal Title

      SIAM Journal on Optimization 19

      Pages: 1881-1893

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A new iterative algorithm for the variational inequality problem over the fixed point set of a firmly nonexpansive mapping2009

    • Author(s)
      Hideaki IIDUKA
    • Journal Title

      Optimization (Accepted)

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Strong convergence for an iterative method for the triple-hierarchical constrained optimization problem2009

    • Author(s)
      Hideaki IIDUKA
    • Journal Title

      Nonlinear Analysis, Special Issue : WCNA 2008 (Accepted)

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Projection method for variational inequality problems for monotone operators2009

    • Author(s)
      Hideaki IIDUKA
    • Journal Title

      Proceedings of the Asian Conference on Nonlinear Analysis and Optimization (Accepted)

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 不動点集合上の凸最適化問題に関する共役勾配法2009

    • Author(s)
      飯塚秀明
    • Journal Title

      非線形解析学と凸解析学の研究 (Accepted)

    • Related Report
      2008 Annual Research Report
  • [Journal Article] Weak convergence of a projection algorithm for variational inequalitiesin a Banach space2008

    • Author(s)
      Hideaki IIDUKA, Wataru TAKAHASHI
    • Journal Title

      Journal of Mathematical Analysis and Applications 339

      Pages: 668-679

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Strong convergence studied by a hybrid type method for monotone operators in a Banach space2008

    • Author(s)
      Hideaki IIDUKA, Wataru TAKAHASHI
    • Journal Title

      Nonlinear Analysis

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Asubgradient-type method for the equilibrium problem over the fixed point set and its applications2008

    • Author(s)
      Hideaki IIDiTKA, Isao YAMADA
    • Journal Title

      Optimization

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Hybrid conjugate gradient method for the convex optimization problem over the fixed point set of a nonexpansive mapping2008

    • Author(s)
      Hideaki IIDUKA
    • Journal Title

      Journal of Optimization Theory and Applications (Accepted)

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] An ergodic algorithm for power control for CDMA data networks2008

    • Author(s)
      Hideaki IIDUKA, Isao YAMADA
    • Journal Title

      電子情報通信学会技術研究報告CAS2007-125-161[回路とシステム] 107

      Pages: 17-22

    • Related Report
      2007 Annual Research Report
  • [Presentation] Weak convergence of an iterative algorithm for the variational inequality problem over the fixed point set2009

    • Author(s)
      Hideaki IIDUKA
    • Organizer
      The Sixth International Conference on Nonlinear Analysis and Convex Analysis
    • Place of Presentation
      Tokyo Institute of Technology, Tokyo, Japan
    • Year and Date
      2009-03-30
    • Related Report
      2008 Annual Research Report
  • [Presentation] Iterative methods for variational inequality problems over fixed point sets2008

    • Author(s)
      Hideaki IIDUKA
    • Organizer
      東京工業大学グローバルCOEプログラム計算世界観の深化と展開 Comp View シンポジウム2008(Invited)
    • Place of Presentation
      Tokyo Institute of Technology, Tokyo, Japan
    • Year and Date
      2008-12-04
    • Related Report
      2008 Annual Research Report
  • [Presentation] An iterative method for the triple-hierarchical optimization problem and its applications2008

    • Author(s)
      Hideaki IIDUKA
    • Organizer
      Asian Conference on Nonlinear Analysis and Optimization
    • Place of Presentation
      Kunibiki Messe, Matue, Japan
    • Year and Date
      2008-09-17
    • Related Report
      2008 Annual Research Report
  • [Presentation] An algorithm for the hierarchical constrained optimization problem and its applications2008

    • Author(s)
      Hideaki IIDUKA
    • Organizer
      Nonlinear Analysis and Convex Analysis
    • Place of Presentation
      Kyoto University, Kyoto, Japan
    • Year and Date
      2008-09-01
    • Related Report
      2008 Annual Research Report
  • [Presentation] Iterative algorithms for the hierarchical optimization problem2008

    • Author(s)
      Hideaki IIDUKA
    • Organizer
      The Fifth World Congress of Nonlinear Analysts (Invited)
    • Place of Presentation
      Hyatt Grand Cypress Resort in Orlando, Florida, USA
    • Year and Date
      2008-07-03
    • Related Report
      2008 Annual Research Report
  • [Presentation] An ergodic algorithm for power control for CDMA data networks2008

    • Author(s)
      Hideaki IIDUKA
    • Organizer
      電子情報通信学会研究会
    • Place of Presentation
      山口大学工学部常盤キャンパス
    • Year and Date
      2008-03-07
    • Related Report
      2007 Annual Research Report
  • [Presentation] 制約付き最適化問題に関するハイブリッド共役勾配法について2007

    • Author(s)
      飯塚 秀明
    • Organizer
      日本数学会2007年度秋季総合分科会
    • Place of Presentation
      東北大学川内キャンパス
    • Year and Date
      2007-09-24
    • Related Report
      2007 Annual Research Report
  • [Presentation] 制約付き最適化問題に関するハイブリッド共役勾配法2007

    • Author(s)
      飯塚 秀明
    • Organizer
      日本応用数理学会2007年度年会
    • Place of Presentation
      北海道大学工学部
    • Year and Date
      2007-09-15
    • Related Report
      2007 Annual Research Report
  • [Presentation] Anew algorithm for the convex optimization problem over the fixed point set of a nonexpansive mapping2007

    • Author(s)
      Hideaki IIDUKA
    • Organizer
      Japan-Thailand Joint Seminar on Fixed Point Algorithms in Optimization
    • Place of Presentation
      Tokyo Institute of Technology,Tokyo,Japan
    • Year and Date
      2007-09-06
    • Related Report
      2007 Annual Research Report
  • [Presentation] The hybrid conjugate gradient method for the constrained optimization problem2007

    • Author(s)
      Hideaki IIDUKA
    • Organizer
      The Eighth International Conference on Fixed Point Theory and its Applications
    • Place of Presentation
      Chiang Mai University,Chiang Mai,Thailand
    • Year and Date
      2007-07-19
    • Related Report
      2007 Annual Research Report
  • [Remarks]

    • URL

      http://www.ndrc.kyutech/ac.jp/~iiduka/

    • Related Report
      2008 Annual Research Report

URL: 

Published: 2007-04-01   Modified: 2024-03-26  

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