• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Study on Practical Algorithms for Nonlinear Integer Programs Based on Discrete Convex Analysis Approach

Research Project

Project/Area Number 18740042
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionTohoku University

Principal Investigator

SHIOURA Akiyoshi  Tohoku University, 大学院情報科学研究科, 准教授 (10296882)

Project Period (FY) 2006 – 2008
Project Status Completed (Fiscal Year 2008)
Budget Amount *help
¥3,760,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥360,000)
Fiscal Year 2008: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2007: ¥1,200,000 (Direct Cost: ¥1,200,000)
Fiscal Year 2006: ¥1,000,000 (Direct Cost: ¥1,000,000)
Keywords組合せ最適化 / 非線形関数 / 整数計画 / 離散凸関数 / 近似解法 / アルゴリズム / マトロイド / 劣モジュラ関数 / 非線形計画 / 凸解析 / 凸関数 / 離散凸解析
Research Abstract

整数計画問題とは,与えられた制約条件を満たす整数ベクトルの中から,与えられた目的関数を最小化(または最大化)する解を求める問題である.一般に整数計画問題は短時間で解くことが困難である,ということが理論的にも現実的にも知られている.とくに,目的関数と条件が非線形関数で与えられる非線形整数計画問題は,解くことが最も困難な整数計画のクラスである.本研究では,様々な非線形整数計画問題に対して,その良質な近似解を短時間で求めるアルゴリズムを提案した.

Report

(4 results)
  • 2008 Annual Research Report   Final Research Report ( PDF )
  • 2007 Annual Research Report
  • 2006 Annual Research Report
  • Research Products

    (24 results)

All 2009 2008 2007 2006 Other

All Journal Article (10 results) (of which Peer Reviewed: 7 results) Presentation (14 results)

  • [Journal Article] On the Pipage Rounding Algorithm for Submodular Function Maximization2009

    • Author(s)
      Akiyoshi Shioura
    • Journal Title

      Discrete Mathematics, Algorithms, and Applications 1

      Pages: 1-23

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] On the Pipage Rounding Algorithm for Submodular Function Maximization2009

    • Author(s)
      Akiyoshi Shioura
    • Journal Title

      Discrete Mathematics, Algorithms and Applications 1(出版予定)

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Note on the Continuity of M-convex and L-convex Functions in Continuous Variables2008

    • Author(s)
      Kazuo Murota, Akiyoshi Shioura
    • Journal Title

      Journal of the Operations Research Society of Japan 51

      Pages: 265-273

    • NAID

      110007008320

    • Related Report
      2008 Annual Research Report 2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Polynomial-time Algorithms for Linear and Convex Optimization on Jump Systems2007

    • Author(s)
      Akiyoshi Shioura, Ken'ichiro Tanaka
    • Journal Title

      SIAM Journal on Discrete Mathematics 21

      Pages: 504-522

    • NAID

      120002337749

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Polynomial-time Algorithms for Linear and Convex Optimization on Jump Systems2007

    • Author(s)
      A. Shioura, K. Tanaka
    • Journal Title

      SIAM Journal on Discrete Mathematics 21

      Pages: 504-522

    • NAID

      120002337749

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Efficiently Pricing European-Asian Options: Ultimate Implementation and Analysis of the AMO Algorithm2006

    • Author(s)
      Akiyoshi Shioura, Takeshi Tokuyama
    • Journal Title

      Information Processing Letters 100

      Pages: 213-219

    • NAID

      110002812022

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Efficient Strategy Proof Fair Allocation Algorithms2006

    • Author(s)
      Akiyoshi Shioura, Ning Sun, and Zaifu Yang
    • Journal Title

      Journal of the Operations Research Society of Japan 49

      Pages: 144-150

    • NAID

      110004737675

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Efficiently Pricing European-Asian Options : Ultimate Implementation and Analysis of the AMO Algorithm2006

    • Author(s)
      Akiyoshi Shioura, Takeshi Tokuyama
    • Journal Title

      Information Processing Letters 100巻6号

      Pages: 213-219

    • NAID

      110002812022

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Efficient Strategy Proof Fair Allocation Algorithms2006

    • Author(s)
      Akiyoshi Shioura, Ning Sun, Zaifu Yang
    • Journal Title

      Journal of the Operations Research Society of Japan 49巻2号

      Pages: 144-150

    • NAID

      110004737675

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Polynomial-time Algorithms for Linear and Convex Optimization on Jump Systems

    • Author(s)
      Akiyoshi Shioura, Ken'ichiro Tanaka
    • Journal Title

      SIAM Journal on Discrete Mathematics (掲載予定)

    • NAID

      120002337749

    • Related Report
      2006 Annual Research Report
  • [Presentation] A Fast Divide-and-Conquer Algorithm for Polymatroid Optimization and Its Application to Preemptive Scheduling Problems with Controllable Processing Times2009

    • Author(s)
      塩浦昭義
    • Organizer
      統計数理研究所研究集会「最適化:モデリングとアルゴリズム」
    • Place of Presentation
      統計数理研究所
    • Year and Date
      2009-03-25
    • Related Report
      2008 Final Research Report
  • [Presentation] Divide-and-Conquer Approach for Preemptive Scheduling Problems with Controllable Processing Times2008

    • Author(s)
      塩浦昭義
    • Organizer
      電子情報通信学会コンピュテーション研究会
    • Place of Presentation
      東北大学
    • Year and Date
      2008-10-10
    • Related Report
      2008 Final Research Report
  • [Presentation] Divide-and-Conquer Approach for Preemptive Scheduling ,Problems with Controllable Processing Times2008

    • Author(s)
      塩浦昭義
    • Organizer
      電子情報通信学会コンピュテーション研究会
    • Place of Presentation
      東北大学
    • Year and Date
      2008-10-10
    • Related Report
      2008 Annual Research Report
  • [Presentation] Fast Divide-and-Conquer Algorithms for Preemptive Scheduling Problems with Controllable Processing Times: A Polymatroid Optimization Approach2008

    • Author(s)
      塩浦昭義
    • Organizer
      16th European Symposium on Algorithms
    • Place of Presentation
      ドイツ,カールスルーエ大学
    • Year and Date
      2008-09-17
    • Related Report
      2008 Final Research Report
  • [Presentation] Fast Divide-and-Conquer Algorithms for Preemptive Scheduling Problem s with Controllable Processing Times : A Polymatroid Optimization Approach2008

    • Author(s)
      塩浦昭義
    • Organizer
      16th European Symposium on Algorithms
    • Place of Presentation
      ドイツ, カールスルー工大学
    • Year and Date
      2008-09-17
    • Related Report
      2008 Annual Research Report
  • [Presentation] On the Pipage Rounding Algorithm for Submodular Function Maximization: A View from Discrete Convex Analysis2008

    • Author(s)
      塩浦昭義
    • Organizer
      統計数理研究所研究集会「最適化:モデリングとアルゴリズム」
    • Place of Presentation
      統計数理研究所
    • Year and Date
      2008-03-18
    • Related Report
      2008 Final Research Report
  • [Presentation] On the Pipage Rounding Algorithm for Submodular Function Maximization -A View from Discrete Convex Analysis-2008

    • Author(s)
      塩浦昭義
    • Organizer
      統計数理研究所研究集会「最適化:モデリングとアルゴリズム」
    • Place of Presentation
      統計数理研究所
    • Year and Date
      2008-03-18
    • Related Report
      2007 Annual Research Report
  • [Presentation] 劣モジュラ関数最大化に対する近似アルゴリズムと離散凹性2008

    • Author(s)
      塩浦昭義
    • Organizer
      応用数理学会春の研究部会連合発表会
    • Place of Presentation
      首都大学東京
    • Year and Date
      2008-03-09
    • Related Report
      2008 Final Research Report 2007 Annual Research Report
  • [Presentation] 凸費用ネットワークフロー問題の双対に対する効率的なアルゴリズムと そのコンピュータビジョンへの応用2007

    • Author(s)
      塩浦昭義
    • Organizer
      情報処理学会アルゴリズム研究会
    • Place of Presentation
      新潟大学
    • Year and Date
      2007-11-30
    • Related Report
      2008 Final Research Report
  • [Presentation] 凸費用ネットワークフロー問題の双対に対する効率的なアルゴリズムとそのコンピュータビジョンへの応用2007

    • Author(s)
      Vladimir Kolmogorov, 塩浦昭義
    • Organizer
      情報処理学会アルゴリズム研究会
    • Place of Presentation
      新潟大学
    • Year and Date
      2007-11-30
    • Related Report
      2007 Annual Research Report
  • [Presentation] 最小費用テンション問題に対する算法と画像処理への応用2007

    • Author(s)
      塩浦昭義
    • Organizer
      日本オペレーションズリサーチ学会2007年秋季研究発表会
    • Place of Presentation
      政策研究大学院大学
    • Year and Date
      2007-09-27
    • Related Report
      2008 Final Research Report 2007 Annual Research Report
  • [Presentation] アメリカン・アジアンオプションの価格の近似に対する計算幾何学的アプローチ2007

    • Author(s)
      塩浦 昭義
    • Organizer
      情報処理学会アルゴリズム研究会
    • Place of Presentation
      岩手大学
    • Year and Date
      2007-05-11
    • Related Report
      2008 Final Research Report 2007 Annual Research Report
  • [Presentation] Polynomial-Time Algorithms for Convex Optimization on Jump Systems2007

    • Author(s)
      塩浦昭義
    • Organizer
      Workshop on Advances in Optimization
    • Place of Presentation
      東京工業大学
    • Year and Date
      2007-04-20
    • Related Report
      2008 Final Research Report 2007 Annual Research Report
  • [Presentation] ジャンプシステム上の最適化問題に対するアルゴリズム2007

    • Author(s)
      塩浦昭義
    • Organizer
      日本オペレーションズ・リサーチ学会計算と最適化研究部会
    • Place of Presentation
      上智大学
    • Year and Date
      2007-04-14
    • Related Report
      2008 Final Research Report 2007 Annual Research Report

URL: 

Published: 2006-04-01   Modified: 2016-04-21  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi