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I knew the the Marquardt parameter could switch the different edition between Gauss-Newton and steepest descent method , It add a lambda at the diagonal of Hessian matrix but what if the jacobi of different variable have different order of magnitudes ? I mean the diagonal of Hessian , some variable could be 1e10 , but some variable may only have 1e-3, should we add the same lambda to them ?

and one more thing , I guess adding the Marquardt parameter means I add a constraint like lambda * I * dx = 0 , which constraint the dx to 0 ? am I wrong ?

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