Table formulation in Mixed Integer Programming

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I have a mixed integer non-linear optimisation problem. The non-linearity comes from a non-linear equation in which the optimisation variable, $N$, is coupled with another variable that is not optimisation variable, $\tau$, but it is in the objective function.

Therefore, the way I was thinking about to remove the non-linearity is to make a table for different value of $N$ and $\tau$. If I do so, the next step would be formulating the table for different values of $N$ in the problem. Is there any way to formulate the table? Or does anyone have any idea to solve this non-linear optimisation problem?

Thanks