{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:39:59Z","timestamp":1787319599283,"version":"build-2736575974"},"reference-count":24,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2013,1]]},"abstract":"<jats:p>The perimeter functional is known to oppose serious difficulties when it has to be handled within a topology optimization procedure. In this paper, a regularized perimeter functional $\\mbox{Per}_\\varepsilon$, defined for two- and three-dimensional domains, is introduced. On one hand, the convergence of $\\mbox{Per}_\\varepsilon$ to the exact perimeter when $\\varepsilon$ tends to zero is proved. On the other hand, the topological differentiability of $\\mbox{Per}_\\varepsilon$ for $\\varepsilon&gt;0$ is analyzed. These features lead to the design of a topology optimization algorithm suitable for perimeter-dependent objective functionals. Several numerical results illustrate the method.<\/jats:p>","DOI":"10.1137\/100816997","type":"journal-article","created":{"date-parts":[[2013,5,14]],"date-time":"2013-05-14T18:00:30Z","timestamp":1368554430000},"page":"2176-2199","source":"Crossref","is-referenced-by-count":7,"title":["Regularized Perimeter for Topology Optimization"],"prefix":"10.1137","volume":"51","author":[{"given":"Samuel","family":"Amstutz","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2013,5,14]]},"reference":[{"key":"atypb1","doi-asserted-by":"crossref","unstructured":"G. Allaire,<i>Shape Optimization by the Homogenization Method<\/i> Appl. Math. Sci. 146, Springer-Verlag, New York, 2002.","DOI":"10.1007\/978-1-4684-9286-6"},{"key":"atypb2","unstructured":"G. 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