Improved iterative Scaling Method (IIS) detailed __iis

Note:
The goal here is to maximize the difference between the two iterations.
1, the maximum difference value if less than 0, the description has been to the maximum, in the current position to go in any direction, the logarithmic likelihood function will be smaller, we ask is the maximum likelihood function, so we have got the largest likelihood function, at this time the parameter is requested.
2, if the difference is greater than 0, then we are now to maximize the difference, here we get the lower bound of the difference, we can continue to maximize the lower bound, so as to get the maximum difference, to maximize the lower bound, first of all the partial derivative, and make the partial derivative is 0, but here we can see the derivative of the derivation

Contains multiple variables that are not easy to optimize at the same time. So here's a way to draw the following.