As part of my research, I am currently dealing with a convex program whose objective function involves the maximization of the entropy of a random variable (and hence is part of the exponential family of functions) subject to affine equality constraints and a positivity constraint.

I am trying to precisely establish the following quantities:

a> cost per iteration as a function of the problem size,

b>number of iterations necessary to achieve a solution within a fixed tolerance as a function of the problem size.

Is there a reference where I can better understand the successive approximation method to answer these questions? I can also post the exact problem if that is something that will help with getting answers to a> and b>.

Any help with this matter would be greatly appreciated!