I am trying to find the computational complexity of interior point method for a general convex problem and stumbled upon the following complexity in Section 1.3.1 of Convex Optimization by Stephen Boyd: \begin{align} \max\{n^3,n^2m,F\} \end{align} $n$ is the number of optimization variables and $m$ is the number of constraints. $F$ is the cost of evaluating the first and second derivatives of the objective function and constraints. However, I am not sure how this is obtained. Could anyone help me understand how this complexity is derived (or refer me to a paper/book explaining this)?
Also, if my objective function needs $T$ operations to be evaluated. How does the above formula change? Thanks!