I am learning levenberg-marquardt algorithm and in the process implementing the same. I am comfortable with the $Jacobian$, $Hessian$ and step size computation. For trust region implementation, I have the following,

$ if \rho_k < 0.25; { \lambda_{k+1} := ||\delta|| * 0.25} $

$else if \rho > 0.75 \& ||\delta_k|| == |\lambda|; \lambda := min(2*\lambda_k, \lambda_{max})$

$else; \lambda := \lambda$

In this, While all other parameters such as 0.25, 0.75 and $increment$ and $decrement$ parameters are defined, I have no clue on how to arrive at $\lambda_{max}$. If $\lambda_{max}$ can be set arbitrarily to any number how would that impact the convergence and eventually optimization? Could some one shed some light on how to arrive, either algorithmically or heuristically the $\lambda_{max}$?


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