Approximations of Countably Infinite Linear Programs over Bounded Measure Spaces
研究一类可行集为有界测度空间子集的可数无限线性规划，通过求解有限维线性规划来逼近最优值、最优点和最小点，并给出易于计算的误差界，证明误差随问题规模增大而趋于零，可用于计算马尔可夫链的平稳分布、占用测度和退出分布。
Abstract\n\nWe study a class of countably infinite linear programs (CILPs) whose feasible sets are bounded subsets of appropriately defined spaces of measures. The optimal value, optimal points, and minimal points of these CILPs can be approximated by solving finite-dimensional linear programs. We show how to construct finite-dimensional programs that lead to approximations with easy-to-evaluate error bounds, and we prove that the errors converge to zero as the size of the finite-dimensional programs approaches that of the original problem. We discuss the use of our methods in the computation of the stationary distributions, occupation measures, and exit distributions of Markov chains.\n\n\nRead More: https://epubs.siam.org/doi/10.1137/19M1268847\n\n \n\n \n\n