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Study on globally convergent algorithms for solving nonlinear systems using mathematical techniques

Research Project

Project/Area Number 18K04151
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Review Section Basic Section 21020:Communication and network engineering-related
Research InstitutionChuo University

Principal Investigator

Yamamura Kiyotaka  中央大学, 理工学部, 教授 (30182603)

Project Period (FY) 2018-04-01 – 2023-03-31
Project Status Completed (Fiscal Year 2022)
Budget Amount *help
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2022: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2021: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2020: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2018: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Keywords非線形理論・回路 / 非線形数値解析 / 大規模集積回路 / 全解探索 / 数理計画法 / 整数計画法 / ホモトピー法 / 区間解析 / 回路シミュレーション / 予測子修正子法 / 非線形システム
Outline of Final Research Achievements

In this project, we developed efficient and globally-convergent algorithms for solving large-scale nonlinear circuits and systems. We first proposed an efficient homotopy method for solving nonlinear circuits, and proved its global convergence property. By this method, bipolar analog integrated circuits with more than 20,000 elements could be solved with the theoretical guarantee of global convergence. We next proposed an efficient algorithm for finding all solutions of nonlinear circuits using linear programming. By this algorithm, all solutions of large-scale systems where the number of variables is several thousands could be found in practical computation time. We further proposed an efficient method for finding all solution sets of nonlinear circuits using integer programming. By this method, complete analysis of nonlinear circuits can be performed easily without making complicated programs. These algorithms are excellent at both efficiency and practicality.

Academic Significance and Societal Importance of the Research Achievements

大規模集積回路をはじめとする非線形システムの解析問題は科学技術における重要かつ難しい問題の一つで、現在でも「解に収束しない」「効率的な解法が存在しない」「実用化が難しい」などの困難が生じている。本研究では、非線形システムの解析問題の中でも特に難しいとされる「解に収束することが理論的に保証された解法」「すべての解を確実に求めることができる解法」などの大域的求解法の分野を対象に、数理的手法(ホモトピー法、線形計画法、整数計画法など)を用いた非線形システムの“効率的で実用的な”大域的求解法の開発を行い、集積回路設計、ニューラルネットワーク、AIなどの分野の発展に貢献した。

Report

(6 results)
  • 2022 Annual Research Report   Final Research Report ( PDF )
  • 2021 Research-status Report
  • 2020 Research-status Report
  • 2019 Research-status Report
  • 2018 Research-status Report
  • Research Products

    (20 results)

All 2021 2019 2018

All Journal Article (11 results) (of which Int'l Joint Research: 5 results,  Peer Reviewed: 9 results,  Open Access: 4 results) Presentation (9 results) (of which Int'l Joint Research: 7 results,  Invited: 1 results)

  • [Journal Article] An efficient algorithm for finding all solutions of nonlinear equations using parallelogram LP test2021

    • Author(s)
      Kiyotaka Yamamura
    • Journal Title

      Journal of Computational and Applied Mathematics

      Volume: 382 Pages: 113080-113080

    • DOI

      10.1016/j.cam.2020.113080

    • Related Report
      2021 Research-status Report 2020 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Finding all solution sets of piecewise-linear interval equations using an integer programming solver2021

    • Author(s)
      Kiyotaka Yamamura
    • Journal Title

      Journal of Computational and Applied Mathematics

      Volume: 372 Pages: 1-10

    • DOI

      10.1016/j.cam.2019.112616

    • Related Report
      2020 Research-status Report 2019 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] An efficient method for finding all characteristic curves of piecewise-linear resistive circuits using integer programming2019

    • Author(s)
      Takumi Kuramoto and Kiyotaka Yamamura
    • Journal Title

      Proceedings of 2019 IEEE Asia Pacific Conference on Postgraduate Research in Microelectronics and Electronics (PrimeAsia)

      Volume: 1 Pages: 41-44

    • DOI

      10.1109/primeasia47521.2019.8950733

    • Related Report
      2019 Research-status Report
    • Peer Reviewed
  • [Journal Article] Finding all characteristic curves of piecewise-linear resistive circuits using an integer programming solver2019

    • Author(s)
      Takumi Kuramoto and Kiyotaka Yamamura
    • Journal Title

      Proceedings of 2019 IEEE Workshop on Nonlinear Circuit Networks

      Volume: 1 Pages: 79-82

    • Related Report
      2019 Research-status Report
    • Peer Reviewed
  • [Journal Article] ホモトピー法への感謝,すべての解への憧れ2019

    • Author(s)
      山村清隆
    • Journal Title

      電子情報通信学会総合大会講演論文集

      Volume: NK-1-1

    • Related Report
      2018 Research-status Report
  • [Journal Article] Finding all solution sets of piecewise-linear interval equations using an integer programming solver2018

    • Author(s)
      Kiyotaka Yamamura
    • Journal Title

      Book of Abstracts, SCAN2018 (The 18th International Symposium on Scientific Computing, Computer Arithmetic, and Verified Numerical Computations)

      Volume: 1 Pages: 36-37

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] An efficient variable-gain homotopy method for finding DC operating points of transistor circuits2018

    • Author(s)
      Kiyotaka Yamamura and Takumi Shimada
    • Journal Title

      Proceedings of 2018 IEEE Asia Pacific Conference on Circuits and Systems

      Volume: 1 Pages: 235-238

    • DOI

      10.1109/apccas.2018.8605634

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Finding all solutions of piecewise-linear resistive circuits using triangular LP test2018

    • Author(s)
      Kiyotaka Yamamura and Hiroki Takahara
    • Journal Title

      Proceedings of 2018 IEEE Asia Pacific Conference on Circuits and Systems

      Volume: 1 Pages: 243-246

    • DOI

      10.1109/apccas.2018.8605636

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Finding all solutions of piecewise-linear resistive circuits using rectangular and triangular LP tests2018

    • Author(s)
      Kiyotaka Yamamura and Hiroki Takahara
    • Journal Title

      Proceedings of 2018 IEEE Workshop on Nonlinear Circuit Networks

      Volume: 1 Pages: 62-65

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] An efficient method for finding all characteristic curves of piecewise-linear resistive circuits using integer programming2018

    • Author(s)
      Kiyotaka Yamamura and Yuichiro Takane
    • Journal Title

      Proceedings of 2018 IEEE Workshop on Nonlinear Circuit Networks

      Volume: 1 Pages: 66-69

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] An efficient variable-gain homotopy method for finding DC operating points of transistor circuits2018

    • Author(s)
      Kiyotaka Yamamura and Takumi Shimada
    • Journal Title

      電子情報通信学会技術研究報告

      Volume: 1 Pages: 75-79

    • Related Report
      2018 Research-status Report
  • [Presentation] An efficient method for finding all characteristic curves of piecewise-linear resistive circuits using integer programming2019

    • Author(s)
      Takumi Kuramoto and Kiyotaka Yamamura
    • Organizer
      2019 IEEE Asia Pacific Conference on Postgraduate Research in Microelectronics and Electronics (PrimeAsia)
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research
  • [Presentation] Finding all characteristic curves of piecewise-linear resistive circuits using an integer programming solver2019

    • Author(s)
      Takumi Kuramoto and Kiyotaka Yamamura
    • Organizer
      2019 IEEE Workshop on Nonlinear Circuit Networks
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research
  • [Presentation] ホモトピー法への感謝,すべての解への憧れ2019

    • Author(s)
      山村清隆
    • Organizer
      2019年電子情報通信学会総合大会
    • Related Report
      2018 Research-status Report
    • Invited
  • [Presentation] Finding all solution sets of piecewise-linear interval equations using an integer programming solver2018

    • Author(s)
      Kiyotaka Yamamura
    • Organizer
      SCAN2018 (The 18th International Symposium on Scientific Computing, Computer Arithmetic, and Verified Numerical Computations)
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research
  • [Presentation] An efficient variable-gain homotopy method for finding DC operating points of transistor circuits2018

    • Author(s)
      Kiyotaka Yamamura and Takumi Shimada
    • Organizer
      2018 IEEE Asia Pacific Conference on Circuits and Systems
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research
  • [Presentation] Finding all solutions of piecewise-linear resistive circuits using triangular LP test2018

    • Author(s)
      Kiyotaka Yamamura and Hiroki Takahara
    • Organizer
      2018 IEEE Asia Pacific Conference on Circuits and Systems
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research
  • [Presentation] Finding all solutions of piecewise-linear resistive circuits using rectangular and triangular LP tests2018

    • Author(s)
      Kiyotaka Yamamura and Hiroki Takahara
    • Organizer
      2018 IEEE Workshop on Nonlinear Circuit Networks
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research
  • [Presentation] An efficient method for finding all characteristic curves of piecewise-linear resistive circuits using integer programming2018

    • Author(s)
      Kiyotaka Yamamura and Yuichiro Takane
    • Organizer
      2018 IEEE Workshop on Nonlinear Circuit Networks
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research
  • [Presentation] An efficient variable-gain homotopy method for finding DC operating points of transistor circuits2018

    • Author(s)
      Kiyotaka Yamamura and Takumi Shimada
    • Organizer
      電子情報通信学会 非線形問題研究会
    • Related Report
      2018 Research-status Report

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Published: 2018-04-23   Modified: 2024-01-30  

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