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The paper is actually the same, which the current Nelder-Mead is based on; compared to that LTMADS seems quite technical, so I am not yet sure how much effort such an implementation would be. To me at first read it seems to be a serious effort to realise that, unless we can use an existing LTMADS step in the tangent space in each iteration.
Here is the paper: https://optimization-online.org/2007/08/1742/ .
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