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

A Study on Acceleration and Stabilization of the Levenberg-Marquardt Method

Research Project

Project/Area Number 14550402
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field System engineering
Research Institution九州芸術工科大学

Principal Investigator

SAKAMOTO Hiroyasu  Kyushu University, Department of Design, Professor, 大学院・芸術工学研究院, 教授 (70112357)

Project Period (FY) 2002 – 2003
Project Status Completed (Fiscal Year 2003)
Budget Amount *help
¥2,000,000 (Direct Cost: ¥2,000,000)
Fiscal Year 2003: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 2002: ¥1,400,000 (Direct Cost: ¥1,400,000)
KeywordsNonlinear optimization method / Least squares method / Interfacial tension measurement system / Levenberg-Marquardt method / Quasi-Newton-Gauss method / Levenberg-Marquardt Morrison method / Multiple local minima problem / Surface shape of a cost function / 非線形計画法 / モリソン法 / 最急降下法 / ニュートン・ガウス法 / 最小2乘法
Research Abstract

In order to accelerate and stabilize the Levenberg-Marquardt (LM) method (including LMM method), this research has proposed extensions of the methods from the conventional constraint (C1) : [M-factor times unit matrix] to the new constraints of (C2) : [a diagonal matrix] and (C3) : [a square root matrix of squared Jacobian], and has verified its high efficiency. Simultaneously, the proposed method has been employed in a surface tension measurement system which had actually motivated this research, and has attained 3 to 10 times faster convergence. Currently, the system is going to go into production.
Numerical results have certified that the proposed constraints (C2, C3) can fit to local surface shape of cost function much better than (C1) and thus attain acceleration and stabilization. Especially because (C3) shows the best fit, it is suitable for the purpose where multiple local minima are searched by controlling search area with distributed initial values and the global minimum is found by comparing those local minima.
A final paper was submitted to IEICE. One of two referees comments that "the paper is so interesting that it is suitable to be accepted as a paper." But the other referee ignores our claim and comments that our proposal "is merely a damped Gauss-Newton method and has no global convergence property," without showing any reasonable ground. Further, based on ignorance of solution method of over-constrained linear equations, his comment says that updating parameter vector is always zero. Thus, the submitted paper has been rejected. However, if his comment were true, it is clear that any LMM method becomes invalid. His comment is obviously false. Currently, making contact with a co-editor, we are going to re-submit a revised paper.

Report

(3 results)
  • 2003 Annual Research Report   Final Research Report Summary
  • 2002 Annual Research Report
  • Research Products

    (21 results)

All Other

All Publications (21 results)

  • [Publications] Hiroyasu SAKAMOTO: "A Simple Acceleration Technique of Levenberg-Marquardt Method"International Symposium on Nonlinear Theory and its Applications. 439-442 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] 坂本 博康: "画像処理による表面張力の実時間測定法"映像情報メディア学会誌. 56. 1643-1650 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] 坂本 博康: "レーベンバーグ・マルカート法の高速化の一方法"電子情報通信学会誌技術研究報告[非線形問題]. 102. 53-58 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] 坂本 博康: "新しい拘束条件によるレーベンバーグ・マルカート法の高速化と安定化の方法"電気関係学会九州支部連合大会講演論文集. 05-2P-12 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] 桑原 梓: "メガピクセルカメラによる表面張力測定装置の高精度化"電気関係学会九州支部連合大会講演論文集. 01-1A-10 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] 坂本 博康: "曲線当てはめによる静滴の界面張力測定法"電子情報通信学会2004年総合大会講演論文集. D-11-131 (2004)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Hiroyasu Sakamoto, Azusa Kuwahara, Yoshiteru Hayami: "A Simple Acceleration Technique of Levenberg-Marquardt Method"International Symposium on Nonlinear Theory and its Applications. 439-442 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Hiroyasu Sakamoto, Akihiro Murao, Yoshiteru Hayami: "Real-time Measurement of Interfacial Tension by Image Processing"The Journal of the Institute of Image information and Television Engineers. 56-10. 1643-1650 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Hiroyasu Sakamoto, Azusa Kuwahara, Katsuya Matsumoto, Yoshiteru Hayami: "A Technique for Accelerating Levenberg-Marquardt Method"Technical Report of IEICE. NLP2002-145. 53-58 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Azusa Kuwahara, Hiroyasu Sakamoto, Yoshiteru Hayami: "Improving Accuracy of Interfacial Tension Measurement System by Using a Mega-pixel Camera"Record of 2003 Joint Conference of Electrical and Electronics Engineers in Kyushu. 01-1A-10. (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Hiroyasu Sakamoto, Katsuya Matsumoto: "An Acceleration and Stabilization Technique of the Levenberg-Marquardt Method by a New Constraint Condition"Record of 2003 Joint Conference of Electrical and Electronics Engineers in Kyushu. 05-2P-12. (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Hiroyasu Sakamoto, Yoshiteru Hayami, Ryo Murakami, Makoto Aratono: "An Interfacial Tension Measurement Method for Sessile Drops by Curve Fitting"Proceedings of the 2004 IEICE General Conference. D-11. 131 (2004)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Hiroyasu SAKAMOTO: "A Simple Acceleration Technique of Levenberg-Marquardt Method"International Symposium on Nonlinear Theory and its Applications. 439-442 (2002)

    • Related Report
      2003 Annual Research Report
  • [Publications] 坂本 博康: "画像処理による表面張力の実時間測定法"映像情報メディア学会誌. 56・10. 1643-1650 (2002)

    • Related Report
      2003 Annual Research Report
  • [Publications] 坂本 博康: "レーベンバーグ・マルカート法の高速化の一方法"電子情報通信学会技術研究報告[非線形問題]. 102・725. 53-58 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] 坂本 博康: "新しい拘束条件によるレーベンバーグ・マルカート法の高速化と安定化の方法"電気関係学会九州支部第56回連合大会講演論文集. 05-2P-12 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] 桑原 梓: "メガピクセルカメラによる表面張力測定装置の高精度化"電気関係学会九州支部第56回連合大会講演論文集. 01-1A-10 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] 坂本 博康: "曲線当てはめによる静滴の界面張力測定法"電子情報通信学会2004年総合大会講演論文集. (in press). (2004)

    • Related Report
      2003 Annual Research Report
  • [Publications] Hiroyasu SAKAMOTO: "A Simple Acceleration Technique of Levenberg-Marquardt Method"International Symposium on Nonlinear Theory and its Applications. 439-442 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] 坂本 博康: "画像処理による表面張力の実時間測定法"映像情報メディア学会誌. 56・10. 1643-1650 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] 坂本 博康: "レーベンバーグ・マルカート法の高速化の一方法"電子情報通信学会技術研究報告[非線形問題]. 102・725. 53-58 (2003)

    • Related Report
      2002 Annual Research Report

URL: 

Published: 2002-04-01   Modified: 2016-04-21  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi