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The approach is applied to a mechanical shape optimization problem in which the leader decides on an optimal material distribution to minimize a tracking-type cost functional, whereas the follower chooses forces from an admissible set to maximize a compliance objective. The material distribution is considered to be stochastically perturbed in the actual construction phase. Computational results illustrate the bilevel optimization concept and demonstrate the interplay of follower and leader in shape design and testing.<\/jats:p>","DOI":"10.1007\/s10107-021-01736-w","type":"journal-article","created":{"date-parts":[[2021,11,29]],"date-time":"2021-11-29T10:02:59Z","timestamp":1638180179000},"page":"1125-1151","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["A pessimistic bilevel stochastic problem for elastic shape optimization"],"prefix":"10.1007","volume":"198","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6745-0784","authenticated-orcid":false,"given":"Johanna","family":"Burtscheidt","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2617-0855","authenticated-orcid":false,"given":"Matthias","family":"Claus","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7987-9174","authenticated-orcid":false,"given":"Sergio","family":"Conti","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Martin","family":"Rumpf","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8069-4713","authenticated-orcid":false,"given":"Josua","family":"Sassen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2486-7111","authenticated-orcid":false,"given":"R\u00fcdiger","family":"Schultz","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,11,29]]},"reference":[{"issue":"2","key":"1736_CR1","doi-asserted-by":"publisher","first-page":"371","DOI":"10.1007\/BF00941574","volume":"68","author":"JF Bard","year":"1991","unstructured":"Bard, J.F.: Some properties of the bilevel programming problem. 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