I'm interested in knowing practical optimization methods which resemble what done in NUM (network utility maximization). Basically, I envision a network in which sources' sending rate is regulated by a central autority with the aim of maximazing the utility associated to source's rate.
The main constrain regard the links' capacities. If they are known the problem would resemble NUM theory.However, in my case of study they are not known a priori but inferred by an index (e.g. packet loss probability).
At first impact, I was thinking that interior methods with barrier function could be a viable solution, however the more I study them the more I'm unsecure of the feasibility.
So my question is what methods or optimization branch would you suggest to study in deep, which could solve such (or similar) class of problems?