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Handling bound constraints by the Levenberg-Marquardt algorithm

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Igor
Igor am 29 Jan. 2019
Bearbeitet: Xingwang Yong am 27 Apr. 2021
Hello,
Could anyone please tell me why the Levenberg-Marquardt algorithm embedded in "lsqnonlin" does not handle bound constraints, while the other one ("trust-region-reflective") does?
There are implementations of the Levenberg-Marquardt algorithm that do accept bound constraints, so what is the principle limitation explaining why this has not been implemented in "lsqnonlin"?
Thank you!
Igor.

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Matt J
Matt J am 29 Jan. 2019
Bearbeitet: Matt J am 29 Jan. 2019
The theory of Levenberg-Marquardt does not define a way to handle bound constraints. If, as you claim, there are modifications of classical LM that support bounds, I surmise that they involve manipulations similar in spirit to what is done in the trust-region algorithm.
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Matt J
Matt J am 29 Jan. 2019
Trust region methods are a very large family, but I don't know of a widely accepted term for Matlab's specific implementation. Maybe you should just cite Coleman and Li.

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Xingwang Yong
Xingwang Yong am 27 Apr. 2021
Bearbeitet: Xingwang Yong am 27 Apr. 2021
In matlab2020b, the doc of lsqcurvefit() has removed "The Levenberg-Marquardt algorithm does not handle bound constraints". So it support bound constraints in LM, can be seen in release notes and doc.

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