Handling bound constraints by the Levenberg-Marquardt algorithm

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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!

Accepted Answer

Matt J
Matt J on 29 Jan 2019
Edited: Matt J on 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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More Answers (1)

Xingwang Yong
Xingwang Yong on 27 Apr 2021
Edited: Xingwang Yong on 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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