{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,4]],"date-time":"2026-08-04T17:40:08Z","timestamp":1785865208716,"version":"3.56.0"},"reference-count":29,"publisher":"Springer Science and Business Media LLC","issue":"2-3","license":[{"start":{"date-parts":[[2005,7,14]],"date-time":"2005-07-14T00:00:00Z","timestamp":1121299200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Program."],"published-print":{"date-parts":[[2005,11]]},"DOI":"10.1007\/s10107-005-0619-y","type":"journal-article","created":{"date-parts":[[2005,7,14]],"date-time":"2005-07-14T16:41:47Z","timestamp":1121359307000},"page":"347-373","source":"Crossref","is-referenced-by-count":106,"title":["Relaxation of an optimal control problem involving a perturbed sweeping process"],"prefix":"10.1007","volume":"104","author":[{"given":"J.F.","family":"Edmond","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"L.","family":"Thibault","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2005,7,14]]},"reference":[{"key":"619_CR1","unstructured":"Balder, E.J.: Lectures on Young measures. Cahiers de math\u00e9matiques de la d\u00e9cision 9514, CEREMADE, Universit\u00e9 Paris-Dauphine, 1995"},{"key":"619_CR2","doi-asserted-by":"crossref","first-page":"286","DOI":"10.1006\/jdeq.1999.3756","volume":"164","author":"Benabdellah","year":"2000","unstructured":"Benabdellah, H.: Existence of solutions to the nonconvex sweeping process. J. Differential Equations 164, 286\u2013295 (2000)","journal-title":"J. Differential Equations"},{"key":"619_CR3","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1016\/S0362-546X(00)00183-8","volume":"48","author":"Bounkhel","year":"2002","unstructured":"Bounkhel, M., Thibault, L.: On various notions of regularity of sets in nonsmooth analysis. Nonlinear Anal. 48, 223\u2013246 (2002)","journal-title":"Nonlinear Anal."},{"key":"619_CR4","unstructured":"Bounkhel, M., Thibault, L.: Nonconvex sweeping process and prox-regularity in Hilbert space. To appear in J. Nonliear Conv. Anal."},{"key":"619_CR5","unstructured":"Castaing, C.: Equation diff\u00e9rentielle multivoque avec contrainte sur l'\u00e9tat dans les espaces de Banach. S\u00e9m. Anal. Convexe Montpellier, Expos\u00e9 13, (1978)"},{"key":"619_CR6","doi-asserted-by":"crossref","unstructured":"Castaing, C., Raynaud de Fitte, P., Valadier, M.: Young Measures on Topological Spaces with Applications in Control Theory and Probability Theory. Kluwer Academic Publishers, Dordrecht, 2004","DOI":"10.1007\/1-4020-1964-5"},{"key":"619_CR7","first-page":"217","volume":"2","author":"Castaing","year":"2001","unstructured":"Castaing, C., Salvadori, A., Thibault, L.: Functional evolution equations governed by nonconvex sweeping Process. J. Nonlinear Conv. Anal. 2, 217\u2013241 (2001)","journal-title":"J. Nonlinear Conv. Anal."},{"key":"619_CR8","doi-asserted-by":"crossref","unstructured":"Castaing, C., Valadier, M.: Convex Analysis and Measurable Multifunctions. Lecture Notes in Math. Springer-Verlag, Berlin 580, 1977","DOI":"10.1007\/BFb0087685"},{"key":"619_CR9","unstructured":"Clarke, F.H.: Optimization and Nonsmooth Analysis. Wiley Interscience, New York, 1983"},{"key":"619_CR10","unstructured":"Clarke, F.H., Ledyaev, Yu.S., Stern, R.J., Wolenski, P.R.: Nonsmooth Analysis and Control Theory. Springer-Verlag, New York, Inc., 1998"},{"key":"619_CR11","first-page":"117","volume":"2","author":"Clarke","year":"1995","unstructured":"Clarke, F.H., Stern, R.J., Wolenski, P.R.: Proximal smoothness and the lower-C2 property. J. Convex Anal. 2, 117\u2013144 (1995)","journal-title":"J. Convex Anal."},{"key":"619_CR12","doi-asserted-by":"crossref","unstructured":"G. Colombo, V. V. Goncharov, The sweeping processes without convexity. Set-valued Anal. 7 357\u2013374, (1999)","DOI":"10.1023\/A:1008774529556"},{"key":"619_CR13","unstructured":"Edmond, J.F., Thibault, L.: BV solution of nonconvex sweeping process with perturbation (to appear)"},{"key":"619_CR14","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1051\/m2an\/1967010400071","volume":"4","author":"Ghouila-Houri","year":"1967","unstructured":"Ghouila-Houri, A.: Sur la g\u00e9n\u00e9ralisation de la notion de commande d'un syst\u00e8me guidable. Rev. Francaise Informat. Recherche Op\u00e9rationnelle 4, 7\u201332 (1967)","journal-title":"Rev. Francaise Informat. Recherche Op\u00e9rationnelle"},{"key":"619_CR15","unstructured":"Janin, R.: Sur la dualit\u00e9 et la sensibilit\u00e9 dans les probl\u00e8mes de programme math\u00e9matique. Th\u00e8se de doctorat d'\u00e9tat, Paris, 1974"},{"key":"619_CR16","unstructured":"Jawhar, A.: Mesures de transitions et applications. S\u00e9m. Anal. Convexe Montpellier, Expos\u00e9 No. 13, (1984)"},{"key":"619_CR17","unstructured":"Jawhar, A.: Existence de solutions optimales pour les probl\u00e8mes de contr\u00f4le de syst\u00e8mes gouvern\u00e9s par les \u00e9quations diff\u00e9rentielles multivoques. S\u00e9m. Anal. Convexe Montpellier, Expos\u00e9 No. 1, (1985)"},{"key":"619_CR18","doi-asserted-by":"crossref","unstructured":"Monteiro Marques, M.D.P.: Differential inclusions in Nonsmooth Mechanical Problems, Shocks and Dry Friction. Birkh\u00e4user, Basel, (1993)","DOI":"10.1007\/978-3-0348-7614-8"},{"key":"619_CR19","doi-asserted-by":"crossref","first-page":"1235","DOI":"10.1090\/S0002-9947-96-01543-7","volume":"4","author":"Mordukhovich","year":"1996","unstructured":"Mordukhovich, B.S., Shao, Y.: Nonsmooth sequential analysis in Asplund spaces. Trans. Amer. Math. Soc. 4, 1235\u20131279 (1996)","journal-title":"Trans. Amer. Math. Soc."},{"key":"619_CR20","unstructured":"Moreau, J.J.: Rafle par un convexe variable I. S\u00e9m. Anal. Convexe Montpellier, Expos\u00e9 15, (1971)"},{"key":"619_CR21","unstructured":"Moreau, J.J.: Rafle par un convexe variable II. S\u00e9m. Anal. Convexe Montpellier, Expos\u00e9 3, (1972)"},{"key":"619_CR22","first-page":"169","volume":"1","author":"Moreau","year":"1974","unstructured":"Moreau, J.J.: Multi-applications \u00e0 r\u00e9traction finie. Ann. Scuola Norm. Sup. Pisa 1, 169\u2013203 (1974)","journal-title":"Ann. Scuola Norm. Sup. Pisa"},{"key":"619_CR23","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1016\/0022-0396(77)90085-7","volume":"26","author":"Moreau","year":"1977","unstructured":"Moreau, J.J.: Evolution Problem Associated with a Moving Convex Set in a Hilbert Space. J. Differential Equations 26, 347\u2013374 (1977)","journal-title":"J. Differential Equations"},{"key":"619_CR24","doi-asserted-by":"crossref","first-page":"5231","DOI":"10.1090\/S0002-9947-00-02550-2","volume":"352","author":"Poliquin","year":"2000","unstructured":"Poliquin, R.A., Rockafellar, R.T., Thibault, L.: Local differentiability of distance functions. Trans. Amer. Math. Soc. 352, 5231\u20135249 (2000)","journal-title":"Trans. Amer. Math. Soc."},{"key":"619_CR25","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0022-0396(03)00129-3","volume":"193","author":"Thibault","year":"2003","unstructured":"Thibault, L.: Sweeping process with regular and nonregular sets. J. Differential Equations 193, 1\u201326 (2003)","journal-title":"J. Differential Equations"},{"key":"619_CR26","doi-asserted-by":"crossref","first-page":"152","DOI":"10.1007\/BFb0084935","volume":"1446","author":"Valadier","year":"1990","unstructured":"Valadier, M.: Young measures. Methods of Convex Analysis. Lectures Notes in Mathematics 1446, 152\u2013188 (1990)","journal-title":"Methods of Convex Analysis. Lectures Notes in Mathematics"},{"key":"619_CR27","unstructured":"Valadier, M.: Quelques probl\u00e8mes d'entrainement unilat\u00e9ral en dimension finie. S\u00e9m. Anal. Convexe Montpellier Expos\u00e9 No. 8, (1988)"},{"key":"619_CR28","unstructured":"Warga, J.: Optimal Control of differential and functional equations. Academic Press, New York, London, (1972)"},{"key":"619_CR29","first-page":"212","volume":"30","author":"Young","year":"1937","unstructured":"Young, L.C.: Generalized curves and the existence of an attained absolute minimum in the Calculus of Variations. C. R. Soc. Sc. Varsovie 30, 212\u2013234 (1937)","journal-title":"C. R. Soc. Sc. Varsovie"}],"container-title":["Mathematical Programming"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-005-0619-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10107-005-0619-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-005-0619-y","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,4,8]],"date-time":"2020-04-08T07:28:44Z","timestamp":1586330924000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10107-005-0619-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,7,14]]},"references-count":29,"journal-issue":{"issue":"2-3","published-print":{"date-parts":[[2005,11]]}},"alternative-id":["619"],"URL":"https:\/\/doi.org\/10.1007\/s10107-005-0619-y","relation":{},"ISSN":["0025-5610","1436-4646"],"issn-type":[{"value":"0025-5610","type":"print"},{"value":"1436-4646","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,7,14]]}}}