I was reading this help section of matlab's fmincon function that uses interior point algorithm for solving an optimization problem. It says the following optimization problem
is replaced by
To solve the approximate problem, the algorithm uses one of two main types of steps at each iteration:
A direct step in (x, s). This step attempts to solve the KKT equations, Equation 3-2 and Equation 3-3, for the approximate problem via a linear approximation. This is also called a Newton step.
Then it says
As it says the last equation is obtained by trying to solve the KKT conditions. Can anyone help me how it is solved to get the above results?