Approximations of countably-infinite linear programs over bounded measure spaces

We study a class of countably-infinite-dimensional linear programs (CILPs) whose feasible sets are bounded subsets of appropriately defined weighted spaces of measures. We show how to approximate the optimal value, optimal points, and minimal points of these CILPs by solving finite-dimensional linear programs. The errors of our approximations converge to zero as the size of the finite-dimensional program approaches that of the original problem and are easy to bound in practice. We discuss the use of our methods in the computation of the stationary distributions, occupation measures, and exit distributions of Markov~chains

A Learning Theoretic Approach to Energy Harvesting Communication System Optimization

A point-to-point wireless communication system in which the transmitter is equipped with an energy harvesting device and a rechargeable battery, is studied. Both the energy and the data arrivals at the transmitter are modeled as Markov processes. Delay-limited communication is considered assuming that the underlying channel is block fading with memory, and the instantaneous channel state information is available at both the transmitter and the receiver. The expected total transmitted data during the transmitter's activation time is maximized under three different sets of assumptions regarding the information available at the transmitter about the underlying stochastic processes. A learning theoretic approach is introduced, which does not assume any a priori information on the Markov processes governing the communication system. In addition, online and offline optimization problems are studied for the same setting. Full statistical knowledge and causal information on the realizations of the underlying stochastic processes are assumed in the online optimization problem, while the offline optimization problem assumes non-causal knowledge of the realizations in advance. Comparing the optimal solutions in all three frameworks, the performance loss due to the lack of the transmitter's information regarding the behaviors of the underlying Markov processes is quantified