{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,27]],"date-time":"2026-01-27T08:12:41Z","timestamp":1769501561771,"version":"3.49.0"},"reference-count":16,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2020,8,7]],"date-time":"2020-08-07T00:00:00Z","timestamp":1596758400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,8,7]],"date-time":"2020-08-07T00:00:00Z","timestamp":1596758400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Glob Optim"],"published-print":{"date-parts":[[2021,3]]},"DOI":"10.1007\/s10898-020-00941-9","type":"journal-article","created":{"date-parts":[[2020,8,7]],"date-time":"2020-08-07T02:02:16Z","timestamp":1596765736000},"page":"593-615","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A Galerkin approach to optimization in the space of convex and compact subsets of $${\\mathbb {R}}^d$$"],"prefix":"10.1007","volume":"79","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4372-7264","authenticated-orcid":false,"given":"Janosch","family":"Rieger","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,8,7]]},"reference":[{"key":"941_CR1","unstructured":"Alexandrov, A.D.: Convex Polyhedra. Springer Monographs in Mathematics. Springer, Berlin (2005). Translated from the 1950 Russian edition"},{"key":"941_CR2","unstructured":"Antunes, P.R.S., Bogosel, B.: Parametric shape optimization using the support function (2018). arXiv:1809.00254"},{"issue":"2","key":"941_CR3","doi-asserted-by":"publisher","first-page":"A1226","DOI":"10.1137\/19M1256853","volume":"42","author":"S Bartels","year":"2020","unstructured":"Bartels, S., Wachsmuth, G.: Numerical approximation of optimal convex shapes. SIAM J. Sci. Comput. 42(2), A1226\u2013A1244 (2020)","journal-title":"SIAM J. Sci. Comput."},{"key":"941_CR4","doi-asserted-by":"publisher","DOI":"10.1007\/b137163","volume-title":"Variational Methods in Shape Optimization Problems, Volume 65 of Progress in Nonlinear Differential Equations and Their Applications","author":"D Bucur","year":"2005","unstructured":"Bucur, D., Buttazzo, G.: Variational Methods in Shape Optimization Problems, Volume 65 of Progress in Nonlinear Differential Equations and Their Applications. Birkh\u00e4user, Basel (2005)"},{"issue":"1","key":"941_CR5","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1137\/05062679X","volume":"46","author":"K Eppler","year":"2007","unstructured":"Eppler, K., Harbrecht, H., Schneider, R.: On convergence in elliptic shape optimization. SIAM J. Control Optim. 46(1), 61\u201383 (2007)","journal-title":"SIAM J. Control Optim."},{"key":"941_CR6","doi-asserted-by":"publisher","first-page":"263","DOI":"10.6028\/jres.049.027","volume":"49","author":"AJ Hoffman","year":"1952","unstructured":"Hoffman, A.J.: On approximate solutions of systems of linear inequalities. J. Res. Nat. Bur. Stand. 49, 263\u2013265 (1952)","journal-title":"J. Res. Nat. Bur. Stand."},{"key":"941_CR7","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4471-4817-3","volume-title":"Polyhedral and Algebraic Methods in Computational Geometry. Universitext","author":"M Joswig","year":"2013","unstructured":"Joswig, M., Theobald, T.: Polyhedral and Algebraic Methods in Computational Geometry. Universitext. Springer, London (2013)"},{"issue":"2","key":"941_CR8","doi-asserted-by":"publisher","first-page":"368","DOI":"10.1137\/040608039","volume":"16","author":"T Lachland-Robert","year":"2005","unstructured":"Lachland-Robert, T., Oudet, E.: Minimizing within convex bodies using a convex hull method. SIAM J. Optim. 16(2), 368\u2013379 (2005)","journal-title":"SIAM J. Optim."},{"key":"941_CR9","doi-asserted-by":"publisher","DOI":"10.1142\/8527","volume-title":"Undergraduate Convexity","author":"N Lauritzen","year":"2013","unstructured":"Lauritzen, N.: Undergraduate Convexity. World Scientific Publishing, Hackensack (2013)"},{"key":"941_CR10","volume-title":"Linear and Nonlinear Programming, Volume 228 of International Series in Operations Research & Management Science","author":"DG Luenberger","year":"2016","unstructured":"Luenberger, D.G., Ye, Y.: Linear and Nonlinear Programming, Volume 228 of International Series in Operations Research & Management Science, 4th edn. Springer, Cham (2016)","edition":"4"},{"key":"941_CR11","doi-asserted-by":"publisher","first-page":"93","DOI":"10.21136\/CPMF.1939.109441","volume":"68","author":"K Mahler","year":"1939","unstructured":"Mahler, K.: Ein \u00dcbertragungsprinzip f\u00fcr konvexe k\u00f6rper. Casopis Pyest. Mat. Fys. 68, 93\u2013102 (1939)","journal-title":"Casopis Pyest. Mat. Fys."},{"issue":"3","key":"941_CR12","doi-asserted-by":"publisher","first-page":"419","DOI":"10.1215\/00127094-2010-042","volume":"154","author":"F Nazarov","year":"2010","unstructured":"Nazarov, F., Petrov, F., Ryabogin, D., Zvavitch, A.: A remark on the mahler conjecture: local minimality of the unit cube. Duke Math. J. 154(3), 419\u2013430 (2010)","journal-title":"Duke Math. J."},{"issue":"8","key":"941_CR13","doi-asserted-by":"publisher","first-page":"904","DOI":"10.1080\/01630563.2011.587075","volume":"32","author":"J Rieger","year":"2011","unstructured":"Rieger, J.: Discretizations of linear elliptic partial differential inclusions. Numer. Funct. Anal. Optim. 32(8), 904\u2013925 (2011)","journal-title":"Numer. Funct. Anal. Optim."},{"key":"941_CR14","volume-title":"Convex Analysis. Princeton Mathematical Series, No. 28","author":"RT Rockafellar","year":"1970","unstructured":"Rockafellar, R.T.: Convex Analysis. Princeton Mathematical Series, No. 28. Princeton University Press, Princeton (1970)"},{"key":"941_CR15","volume-title":"Convex Bodies: The Brunn\u2013Minkowski Theory, Volume 151 of Encyclopedia of Mathematics and its Applications","author":"R Schneider","year":"2014","unstructured":"Schneider, R.: Convex Bodies: The Brunn\u2013Minkowski Theory, Volume 151 of Encyclopedia of Mathematics and its Applications. Cambridge University Press, Cambridge (2014)"},{"key":"941_CR16","volume-title":"Lectures on Polytopes, Volume 152 of Graduate Texts in Mathematics","author":"GM Ziegler","year":"1995","unstructured":"Ziegler, G.M.: Lectures on Polytopes, Volume 152 of Graduate Texts in Mathematics. Springer, New York (1995)"}],"container-title":["Journal of Global Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-020-00941-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10898-020-00941-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-020-00941-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,8,6]],"date-time":"2021-08-06T23:33:08Z","timestamp":1628292788000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10898-020-00941-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,8,7]]},"references-count":16,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2021,3]]}},"alternative-id":["941"],"URL":"https:\/\/doi.org\/10.1007\/s10898-020-00941-9","relation":{},"ISSN":["0925-5001","1573-2916"],"issn-type":[{"value":"0925-5001","type":"print"},{"value":"1573-2916","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,8,7]]},"assertion":[{"value":"17 September 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 August 2020","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 August 2020","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}