Handling bound constraints by the Levenberg-Marquardt algorithm

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Igor 2019-1-29

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编辑： Xingwang Yong 2021-4-27

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 2019-1-29

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编辑：Matt J 2019-1-29

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 2019-1-29

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.

Igor 2019-1-30

Ok. Thank you!

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Xingwang Yong 2021-4-27

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https://ww2.mathworks.cn/matlabcentral/answers/442037-handling-bound-constraints-by-the-levenberg-marquardt-algorithm#answer_685575

编辑：Xingwang Yong 2021-4-27

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.