publication . Article . Preprint . 2018

Approximations of Countably Infinite Linear Programs over Bounded Measure Spaces

Juan Kuntz; Philipp Thomas; Guy-Bart Stan; Mauricio Barahona;
Open Access
  • Published: 08 Oct 2018 Journal: SIAM Journal on Optimization, volume 31, pages 604-625 (issn: 1052-6234, eissn: 1095-7189, Copyright policy)
  • Publisher: Society for Industrial & Applied Mathematics (SIAM)
  • Country: United Kingdom
Abstract
We study a class of countably-infinite-dimensional 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 distrib...
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Subjects
free text keywords: Theoretical Computer Science, Software, math.OC, math.PR, 0102 Applied Mathematics, 0103 Numerical and Computational Mathematics, Operations Research, Mathematics - Optimization and Control, Mathematics - Probability
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UKRI| Engineering Fellowships for Growth: Systems and control engineering framework for robust and efficient synthetic biology
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  • Funder: UK Research and Innovation (UKRI)
  • Project Code: EP/M002187/1
  • Funding stream: EPSRC
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UKRI| EPSRC Centre for Mathematics of Precision Healthcare
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  • Funder: UK Research and Innovation (UKRI)
  • Project Code: EP/N014529/1
  • Funding stream: EPSRC
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EC| COSY-BIO
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Control Engineering of Biological Systems for Reliable Synthetic Biology Applications
  • Funder: European Commission (EC)
  • Project Code: 766840
  • Funding stream: H2020 | RIA
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UKRI| Doctoral Training Grant
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  • Funder: UK Research and Innovation (UKRI)
  • Project Code: BB/F017510/1
  • Funding stream: BBSRC
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