We consider the setting of sequentially optimizing the average of a sequence of functions, so called online convex optimization.
We consider one of the simplest iterative procedures for solving the (unconstrainted) optimization
We consider a decomposition of the following network utility optimization problem
We argue, in a slightly informal manner, that queueing networks implicitly optimize a utility function subject to constraints on network capacity. We start with the simple example of a closed queueing network and, as we shall discuss, a motivating example is the Transmission Control Protocol which controls the number of packets in transfer on an Internet connection.
The Gale-Eisenberg is a nice example were the distributed decisions of buyers and sellers have an equilibrium which solves an optimization problem.