Approximations of Countably Infinite Linear Programs over Bounded Measure Spaces
- 1. Department of Mathematics and Department of Bioengineering, Imperial College London, London SW7 2AZ, United Kingdom.
- 2. Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom
- 3. Department of Bioengineering, Imperial College London, London SW7 2AZ, United Kingdom
Description
Abstract
We 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.
Read More: https://epubs.siam.org/doi/10.1137/19M1268847
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Kuntz et al 2020 SIAM.pdf
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