2003 Fiscal Year Final Research Report Summary
A Study on Acceleration and Stabilization of the Levenberg-Marquardt Method
| Project/Area Number |
14550402
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
System engineering
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| Research Institution | 九州芸術工科大学 |
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Principal Investigator |
SAKAMOTO Hiroyasu Kyushu University, Department of Design, Professor, 大学院・芸術工学研究院, 教授 (70112357)
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| Project Period (FY) |
2002 – 2003
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| Keywords | Nonlinear 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 |
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| 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.
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Research Products
(12 results)
