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Uncertainty Quantification"],"published-print":{"date-parts":[[2023,12,31]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>We discretize a risk-neutral optimal control problem governed by a linear elliptic partial differential equation with random inputs using a Monte Carlo sample-based approximation and a finite element discretization, yielding finite dimensional control problems. We establish an exponential tail bound for the distance between the finite dimensional problems\u2019 solutions and the risk-neutral problem\u2019s solution. The tail bound implies that solutions to the risk-neutral optimal control problem can be reliably estimated with the solutions to the finite dimensional control problems. Numerical simulations illustrate our theoretical findings.<\/jats:p>","DOI":"10.1137\/22m1503889","type":"journal-article","created":{"date-parts":[[2023,10,18]],"date-time":"2023-10-18T04:45:39Z","timestamp":1697604339000},"page":"1139-1163","source":"Crossref","is-referenced-by-count":4,"title":["Reliable Error Estimates for Optimal Control of Linear Elliptic PDEs with Random Inputs"],"prefix":"10.1137","volume":"11","author":[{"given":"Johannes","family":"Milz","sequence":"first","affiliation":[{"name":"H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2023,10,18]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1137\/16M109870X"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1007\/s10444-018-9653-1"},{"key":"ref3","first-page":"9","volume":"3","author":"Aln\u00e6s M. 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