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INTERIOR-POlNT METHODS FOR OPTIMIZATION PROBLEMS IN SOCIAL SYSTEMS

Research Project

Project/Area Number 08680478
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field 社会システム工学
Research InstitutionTHE INSTITUTE OF STATISTICAL MATHEMATICS

Principal Investigator

MIZUNO Shinji  ISM, DEPT.OF PREDICTION AND CONTROL, 予測制御研究系, 助教授 (90174036)

Co-Investigator(Kenkyū-buntansha) ITO Satoshi  ISM, CENTER FOR DEV.OF STAT.COMP, 計算開発センター, 助教授 (50232442)
TSUCHIYA Takashi  ISM, DEPT.OF PREDICTION AND CONTROL, 予測制御研究系, 助教授 (00188575)
Project Period (FY) 1996 – 1998
Project Status Completed (Fiscal Year 1998)
Budget Amount *help
¥2,700,000 (Direct Cost: ¥2,700,000)
Fiscal Year 1998: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 1997: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 1996: ¥900,000 (Direct Cost: ¥900,000)
KeywordsOPTIMIZATION / SOCIAL SYSTEM / INTERIOR-POINT METHOD / LlNEAR PROGRAMMING / 半正定値計画問題 / 相補性問題
Research Abstract

We have performed a basic research on the interior point methods for solving optimization problems in social systems. In this year, our research mainly devoted to the development of interior point methods for linear programming and semidefinite programming, and devoted to the analysis of the global convergence and the local convergence of these methods.
Most of the optimization problems iii social systems could be modeled as mathematical programming problems. The linear programming problem is the most fundamental mathematical programming problem. We performed two important research on the interior-point methods for linear programming. Firstly, in order to speed up the local convergence of interior point methods, we investigated an algorithm which trace the central path in high degree. As a result of this research, we proposed a high order infeasible interior point algorithm. Secondly, we are interested in the problem to get an initial interior point to perform an algorithm, For this purpose, we investigated two self-dual systems for linear programming, which have trivial initial points.
We studied not only linear programming, but also convex programming, semidefinite programming, and semi-infinite programming. There are many search directions in interior-point methods for solving semidefinite programming problems. We investigated a self-dual subfamily of such directions. We also studied interior-point methods for solving linear and quadratic semi-infinite programming problems and proposed a dual-parameterization algorithm for convex semi-infinite programming.

Report

(4 results)
  • 1998 Annual Research Report   Final Research Report Summary
  • 1997 Annual Research Report
  • 1996 Annual Research Report
  • Research Products

    (20 results)

All Other

All Publications (20 results)

  • [Publications] N.Megiddo,S.Muzuno,T.Tsuchiya: "A Modified Layered-Step Interior:Point Algorithm for Linear Programming" Mathematical Programming. 82・3. 339-355 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] S.Stoer,M.Wochs,S.Mizuno: "High Order Infeasible-Interior-Point Methods for Linear Progamming" Mathematics of Operations Research. 23・4. 832-862 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] R.Monteiro, T.Tsuchiya: "Global Convergence of the Affine Scaling Algorithm for Conrex QP" SIAM Journal on Optimization. 8. 525-552 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 水野 眞治: "ホモトピー法と内点法" 統計数理. 46・2. 335-343 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 土 谷 隆: "半正定値計画問題に対する主双対内点法の自己双対な探索方向族について" 統計数理. 46・2. 283-396 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] N.Megiddo, S.Mizuno, and T.Tsuchiya: "A Modified Layered-Step Interior-Point Algorithm for Linear Programming" Mathematical Programming. Vol.82, No.3. 339-355 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] J.Stoer, M.Wechs, and S.Mizuno: "High Order Infeasible-Interior-Point Methods for Solving Suffcient Linear Complementarity Problems" Mathematics of Operations Research. Vol.23, No.4. 832-862 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] R.D.C.Monteiro and T.Tsuchiya: "Global Convergence of the Affine Scaling Algorithm for Convex Quadratic Programming" SIAM Journal on Optimization. Vol.8. 525-552 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] S.Mizuno : Homotopy Methods and Interior-Point Methods: "Proceedings of the Institute of Statistical Mathematics" Vol.46, No.2. 335-343 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] T.Tsuchiya: "A Scaling Invariant Self-Dual Subfamily of the Monteiro-Tsuchiya family of Search Directions for the Primal-Dual Algorithms for Semidefinite Programming" Proceedings of the Institute of Statistical Mathematics. Vol.46, No.2. 283-296 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] N.Megiddo,S.Mizuno,T.Tsuchiya: "A Modified Layered-Step Interior Point Algorithm for Linear Programming" Mathematical Programming. 82・3. 339-355 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] J.Stoes,M.Wechs,S.Mizuno: "High Order Infeasible-Interior-Point Methods for Linear Programming" Mathematics of Operations Research. 23・4. 832-862 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] R.Monteiro,T.Tsuchiya: "Global Convergence of the Affine Scaling Algorithm for Convex Quadratic Programming" SIAM Journal on Optinization. 8. 525-552 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 水野真治: "ホモトピー法と内点法" 統計数理. 46・2. 335-343 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 土谷隆: "半正定値計画問題に対する主双対内点法の自己双対な探索方向族について" 統計数理. 46・2. 283-296 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] U.Megiddc, S.Mizuno, T.Tsuchiya: "A Modified Layered-Step Inferior-Point Algorithm for Linear Programming" Mathematical Programming. (掲載予定).

    • Related Report
      1997 Annual Research Report
  • [Publications] J.Stoer, M.Wechs, S.Mizuno: "High Order Infeasible-Interior-Point Methods for Solving sufticient LCP" Mathematics of Operations Research. (掲載予定).

    • Related Report
      1997 Annual Research Report
  • [Publications] T.Tsuchiya and R.Monteiro: "Polynomial Convergence of a New Family of Prmal-Ducl Algosithms for SDP" 最適化:モデリングとアルゴリズム. 11. 118-145 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] Shinji Mizuno,Nimrod Megiddo,Takashi Tsuchiya: "A Linear Programming Instance with Many Crossover Events" Journal of Complexity. 12・4. 474-479 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] Josef Stoer, Martin Wechs,Shinji Mizuno: "High Order Infeasible-Interior-Point Methods for Solving Sufficient Linear Complementarity Problems" Research Memorundum. 634. 1-32 (1997)

    • Related Report
      1996 Annual Research Report

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Published: 1996-04-01   Modified: 2016-04-21  

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