{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:26:43Z","timestamp":1787318803047,"version":"build-2736575974"},"reference-count":7,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2010,1]]},"abstract":"<jats:p>In this paper, we focus on the following general shape optimization problem: $\\min\\{J(\\Omega),$ $\\Omega$ convex, $\\Omega\\in\\mathcal{S}_{ad}\\}$, where $\\mathcal{S}_{ad}$ is a set of 2-dimensional admissible shapes and $J:\\mathcal{S}_{ad}\\rightarrow\\mathbb{R}$ is a shape functional. Using a specific parameterization of the set of convex domains, we derive some extremality conditions (first and second order) for this kind of problem. Moreover, we use these optimality conditions to prove that, for a large class of functionals (satisfying a concavity-like property), any solution to this shape optimization problem is a polygon.<\/jats:p>","DOI":"10.1137\/080738581","type":"journal-article","created":{"date-parts":[[2009,11,20]],"date-time":"2009-11-20T22:10:21Z","timestamp":1258755021000},"page":"3003-3025","source":"Crossref","is-referenced-by-count":17,"title":["Polygons as Optimal Shapes with Convexity Constraint"],"prefix":"10.1137","volume":"48","author":[{"given":"Jimmy","family":"Lamboley","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Arian","family":"Novruzi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2009,11,20]]},"reference":[{"key":"R1","unstructured":"T. Bayen,\n                      Optimisation de formes dans la classe des corps de largeur constante et des rotors\n                      , Ph.D. thesis, Universite Pierre et Marie Curie, Paris, 2007. Available online at http:\/\/www. cmap.polytechnique.fr\/$^\\sim$bayen\/Bayen1.pdf."},{"key":"R2","first-page":"343","volume":"4","author":"Buttazzo G.","year":"1997","journal-title":"J. Convex Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0944-6532","issn-type":"print"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.5802\/ambp.204"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1007\/s00205-003-0259-4"},{"key":"R5","unstructured":"A. D. Ioffe and V. M. Tihomirov,\n                      Theory of Extremal Problems\n                      , Stud. Math. Appl. 6, North\u2013Holland, Amsterdam, 1979."},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1002\/1522-2616(200106)226:1<153::AID-MANA153>3.0.CO;2-2"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1007\/BF01582096"}],"container-title":["SIAM Journal on Control and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/080738581","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T12:40:24Z","timestamp":1787316024000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/080738581"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,11,20]]},"references-count":7,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2010,1]]}},"alternative-id":["10.1137\/080738581"],"URL":"https:\/\/doi.org\/10.1137\/080738581","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,11,20]]}}}