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Thereby, we derive upper bounds on the number of samples needed to obtain accurate critical points of the risk-neutral PDE-constrained optimization problem through SAA critical points. We quantify accuracy using expectation and exponential tail bounds. Numerical illustrations are presented.<\/jats:p>","DOI":"10.1137\/22m1512636","type":"journal-article","created":{"date-parts":[[2024,2,23]],"date-time":"2024-02-23T06:07:39Z","timestamp":1708668459000},"page":"844-869","source":"Crossref","is-referenced-by-count":6,"title":["Sample Size Estimates for Risk-Neutral Semilinear PDE-Constrained Optimization"],"prefix":"10.1137","volume":"34","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"}]},{"given":"Michael","family":"Ulbrich","sequence":"additional","affiliation":[{"name":"Technical University of Munich, Department of Mathematics, Boltzmannstr. 3, 85748 Garching b. M\u00fcnchen, Germany."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2024,2,23]]},"reference":[{"key":"ref1","first-page":"9","volume":"3","author":"Aln\u00e6s M. S.","year":"2015","journal-title":"Arch. Numer. 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