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Theory and computational methods of robust optimization

Research Project

Project/Area Number 16540131
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionThe Institute of Statistical Mathematics

Principal Investigator

ITO Satoshi  The Institute of Statistical Mathematics, Department of Mathematical Analysis and Statistical Inference, Associate Professor, 数理・推論研究系, 助教授 (50232442)

Project Period (FY) 2004 – 2006
Project Status Completed (Fiscal Year 2006)
Budget Amount *help
¥3,300,000 (Direct Cost: ¥3,300,000)
Fiscal Year 2006: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2005: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2004: ¥1,200,000 (Direct Cost: ¥1,200,000)
Keywordsrobust optimization / min-max problem / cutting plane method / capacity problem / optimization in measure spaces / robust linear programming / infinite programming / optimal control / 国際情報交換 / 中国 / 最適制御問題 / オーストラリア:中国 / 非線形計画 / 半無限計画 / 微分不可能最適化 / 大域的最適化
Research Abstract

This research project aims at developing efficient algorithms for a class of robust optimization problem based on its theoretical analysis. Such a class of problem is represented in general as a min-max problem involving uncertainty as parameters. We first studied (1) inexact implementations of some numerical algorithms based on the cutting plane strategy, and finally proposed (2) a bilateral cutting plane framework as an ultimate solution form, whose global convergence is shown for a class of optimization problem formulated in a measure space. Furthermore we tried some refinements of the numerical framework towards its more efficient implementation with better local convergence properties. The practical side of this research project includes (3) some applications to semi-infinite programming especially for digital filter design, (4) a theoretical analysis of the asymptotic behavior of the developed framework when applied to a special case whose decision variable is limited to a class of absolutely continuous measure, and (5) some applications to optimal control problems with state variable inequality constraints. We also investigated, as related topics, (6) a type of path-following algorithm based on continuous descent methods and (7) a numerical analysis of the integration of stiff systems of ordinary differential equations.

Report

(4 results)
  • 2006 Annual Research Report   Final Research Report Summary
  • 2005 Annual Research Report
  • 2004 Annual Research Report
  • Research Products

    (16 results)

All 2007 2005 2004

All Journal Article (16 results)

  • [Journal Article] Bilateral cutting plane iteration for solving general capacity problems2007

    • Author(s)
      Ito, S.
    • Journal Title

      Optimization : Modeling and Algorithms 20

      Pages: 243-254

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Bilateral cutting plane iteration for solving general capacity problems2007

    • Author(s)
      Ito, S.
    • Journal Title

      Optimization : Modeling and Algorithms 20 (The Institute of Statistical Mathematics Cooperative Research Report) 203

      Pages: 243-254

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Bilateral cutting plane iteration for solving general capacity problems2007

    • Author(s)
      Ito, S.
    • Journal Title

      統計数理研究所共同研究レポート203「最適化 : モデリングとアルゴリズム20」

      Pages: 243-254

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Tracking control of general nonlinear systems by a direct gradient descent method2005

    • Author(s)
      Shimizu, K., Ito, S, Suzuki, S.
    • Journal Title

      Nonlinear Dynamics and Systems Theory 5/1

      Pages: 91-105

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] 双対2次計画および切除平面法による状態制約最適制御問題の解法2005

    • Author(s)
      伊藤 聡
    • Journal Title

      統計数理 53/2

      Pages: 361-373

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] A numerical solution of state-constrained optimal control problems by dual sequential quadratic programming with cutting plane strategy2005

    • Author(s)
      Ito, S.
    • Journal Title

      Proceedings of the Institute of Statistical Mathematics 53/2

      Pages: 361-373

    • NAID

      120006019086

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] 双対逐次2次計画および切除平面法による状態制約最適制御問題の解法2005

    • Author(s)
      伊藤 聡
    • Journal Title

      統計数理 53・2

      Pages: 361-373

    • NAID

      120006019086

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Tracking control of general nonlinear systems by a direct gradient descent method2005

    • Author(s)
      Shimizu, K.他
    • Journal Title

      Nonlinear Dynamics and Systems Theory 5・1

      Pages: 91-105

    • Related Report
      2004 Annual Research Report
  • [Journal Article] An approximation approach to non-strictly convex quadratic semi-infinite programming2004

    • Author(s)
      Ito, S., Liu, Y., Teo, K.L.
    • Journal Title

      Journal of Global Optimization 30/2-3

      Pages: 195-206

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] A path following method for solving a class of semi-infinite programming problems2004

    • Author(s)
      Ito, S., Shimizu, K.
    • Journal Title

      Abstracts of OCA 2004 n/a

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Nonlinear dynamical programming via direct gradient descent control2004

    • Author(s)
      Shimizu, K., Ito, S.
    • Journal Title

      Proceedings of the 6 ICOTA (cdrom) n/a

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] A path following method for solving a class of semi-infinite programming problems2004

    • Author(s)
      Ito, S., Shimizu, K.
    • Journal Title

      Abstracts of OCA

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Nonlinear dynamical programming via direct gradient descent control2004

    • Author(s)
      Shimizu, K., Ito, S.
    • Journal Title

      Proceedings of the 6th International Conference on Optimisation : Techniques and Applications

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] A path following method for solving a class of semi-infinite programming problems2004

    • Author(s)
      Ito, S.他
    • Journal Title

      Abstracts of OCA 2004

    • Related Report
      2004 Annual Research Report
  • [Journal Article] An approximation approach to non-strictly convex quadratic semi-infinite programming2004

    • Author(s)
      Ito, S.他
    • Journal Title

      Journal of Global Optimization 30・2-3

      Pages: 195-206

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Nonlinear dynamical programming via direct gradient descent control2004

    • Author(s)
      Shimizu, K.他
    • Journal Title

      Proceedings of the 6th International Conference on Optimization : Techniques and Applications (CD-ROM)

    • Related Report
      2004 Annual Research Report

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Published: 2004-04-01   Modified: 2016-04-21  

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