Newton-Raphson convergence for function $f(\gamma)$ with $\gamma \geq0$ constraint.

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I am reading an (engineering) paper that in the part of their solution, They propose a 2-step iterative solution based on Newton-Raphson method for concave function $f$ as below :

1.$\gamma^{t+1}=\gamma^{t}-[H_f(\gamma^{t})]^{-1}\nabla_f(\gamma^{t})$

2.Set the elements of $\gamma$ vector with value less than zero to zero.

Although I am not a mathematician but I am wondering if this method actually converges or at least is expected to converge. I went through the litreture a little but actually I didn't find this way of solving elsewhere.

I want to know does(and why) this (indulgent?) way of solving actually works in practice?