For a number of differing auction settings, we consider the sale of a single item amongst fixed number of auction participants. It is interesting that under a certain game-theoretic construction all these auctions can be seen to be equivalent.
In the Cross Entropy Method, we wish to estimate the likelihood
Here is a random variable whose distribution is known and belongs to a parametrized family of densities . Further is often a solution to an optimization problem.
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.