{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:38:32Z","timestamp":1787337512825,"version":"3.56.0"},"reference-count":14,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","funder":[{"DOI":"10.13039\/501100002261","name":"Russian Foundation for Basic Research","doi-asserted-by":"publisher","award":["16-01-00259"],"award-info":[{"award-number":["16-01-00259"]}],"id":[{"id":"10.13039\/501100002261","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Optim."],"published-print":{"date-parts":[[2018,1]]},"abstract":"<jats:p>We continue the investigation of a general minimal time problem with a convex constant dynamics and a lower semicontinuous extended real-valued target function defined on a Banach space. In this paper we obtain an explicit description of the minimal time projection set in terms of the Legendre--Fenchel conjugate function and provide some sufficient conditions for this set to be nonempty. The single valuedness and Lipschitz property of the minimal time projection are also investigated.<\/jats:p>","DOI":"10.1137\/16m1110212","type":"journal-article","created":{"date-parts":[[2018,1,5]],"date-time":"2018-01-05T16:39:07Z","timestamp":1515170347000},"page":"30-44","source":"Crossref","is-referenced-by-count":7,"title":["Infimal Convolution and Optimal Time Control Problem III: Minimal Time Projection Set"],"prefix":"10.1137","volume":"28","author":[{"given":"Grigorii E.","family":"Ivanov","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lionel","family":"Thibault","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2018,1,5]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-04-03718-3"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1987-0887515-5"},{"key":"atypb3","doi-asserted-by":"crossref","unstructured":"J. M. Borwein and J. D. Vanderwerff,\n                      Convex Functions: Constructions, Characterizations and Counterexamples\n                      , Cambridge University Press, Cambridge, 2010.","DOI":"10.1017\/CBO9781139087322"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1016\/S0362-546X(00)00183-8"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1007\/s11228-010-0151-y"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1023\/B:JOGO.0000026460.10505.dd"},{"key":"atypb7","first-page":"335","volume":"11","author":"Colombo G.","year":"2004","journal-title":"J. Convex Anal."},{"key":"atypb8","doi-asserted-by":"crossref","unstructured":"G. E. Ivanov and L. Thibault,\n                      Infimal Convolution and Optimal Time Control ProblemI:Fre\u0301chet and Proximal Subdifferentials\n                      , Set-Valued Var. Anal.https:\/\/doi.org\/10.1007\/s11228-016-0398-z, 2017.","DOI":"10.1007\/s11228-016-0398-z"},{"key":"atypb9","doi-asserted-by":"crossref","unstructured":"G. E. Ivanov and L. Thibault,\n                      Infimal Convolution and Optimal Time Control Problem II: Limiting Subdifferential\n                      , Set-Valued Var. Anal.https:\/\/doi.org\/10.1007\/s11228-017-0402-2, 2017.","DOI":"10.1007\/s11228-017-0402-2"},{"key":"atypb10","unstructured":"A. Y. Kruger,\n                      Epsilon-Semidifferentials and Epsilon-Normal Elements\n                      , Depon. VINITI 1331-81, Moscow, 1981."},{"key":"atypb11","unstructured":"J. J. Moreau,\n                      Fonctionnelles Convexes\n                      , Colle\u0300ge de France, Paris, 2nd ed., Consiglio Nazionale delle Ricerche and Facolta\u0301 di ingegneria Universita di Roma \u201cTor Vergata,\u201d 1967."},{"key":"atypb12","first-page":"109","volume":"49","author":"Moreau J. J.","year":"1970","journal-title":"J. Math. Pures Appl."},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1137\/0329056"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012996299338"}],"container-title":["SIAM Journal on Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/16M1110212","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:14:47Z","timestamp":1787336087000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/16M1110212"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,1]]},"references-count":14,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2018,1]]}},"alternative-id":["10.1137\/16M1110212"],"URL":"https:\/\/doi.org\/10.1137\/16m1110212","relation":{},"ISSN":["1052-6234","1095-7189"],"issn-type":[{"value":"1052-6234","type":"print"},{"value":"1095-7189","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,1]]}}}