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Optim."],"published-print":{"date-parts":[[2018,1]]},"abstract":"<jats:p>This paper is concerned with necessary and sufficient second-order conditions for finite-dimensional and infinite-dimensional constrained optimization problems. Using a suitably defined directional curvature functional for the admissible set, we derive no-gap second-order optimality conditions in an abstract functional analytic setting. Our theory not only covers those cases where the classical assumptions of polyhedricity or second-order regularity are satisfied but also allows to study problems in the absence of these requirements. As a tangible example, we consider no-gap second-order conditions for bang-bang optimal control problems.<\/jats:p>","DOI":"10.1137\/17m1140418","type":"journal-article","created":{"date-parts":[[2018,7,26]],"date-time":"2018-07-26T13:04:55Z","timestamp":1532610295000},"page":"2097-2130","source":"Crossref","is-referenced-by-count":21,"title":["No-Gap Second-Order Conditions via a Directional Curvature Functional"],"prefix":"10.1137","volume":"28","author":[{"given":"Constantin","family":"Christof","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3098-1503","authenticated-orcid":true,"given":"Gerd","family":"Wachsmuth","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2018,7,26]]},"reference":[{"key":"atypb1","doi-asserted-by":"crossref","unstructured":"L. Ambrosio,\n                      Functions of Bounded Variation and Free Discontinuity Problems\n                      , Oxford University Press, Oxford, 2000.","DOI":"10.1093\/oso\/9780198502456.001.0001"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1007\/s002459900093"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623496306760"},{"key":"atypb4","doi-asserted-by":"crossref","unstructured":"J. F. Bonnans and A. Shapiro,\n                      Perturbation Analysis of Optimization Problems\n                      , Springer, New York, 2000.","DOI":"10.1007\/978-1-4612-1394-9"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012998333724"},{"key":"atypb6","unstructured":"H. Cartan,\n                      Calcul Diffe\u0301rentiel\n                      , Hermann, Paris, 1967."},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1137\/120862892"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1137\/110840406"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1365\/s13291-014-0109-3"},{"key":"atypb10","unstructured":"E. Casas, D. Wachsmuth, and G. Wachsmuth,\n                      Second Order Analysis and Numerical Approximation for Bang-Bang Bilinear Control Problems\n                      , preprint,https:\/\/arxiv.org\/abs\/1707.06880, 2017."},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1137\/16M1099674"},{"key":"atypb12","unstructured":"C. Christof and C. Meyer,\n                      Differentiability Properties of the Solution Operator to an Elliptic Variational Inequality of the Second Kind\n                      , Technical report, Ergebnisberichte des Instituts fu\u0308r Angewandte Mathematik, TU Dortmund, 2016."},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1007\/s10589-010-9365-z"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1992-1088019-1"},{"key":"atypb15","doi-asserted-by":"crossref","unstructured":"L. Evans and R. Gariepy,\n                      Measure Theory and Fine Properties of Functions\n                      , revised ed., CRC Press, Boca Raton, FL, 2015.","DOI":"10.1201\/b18333"},{"key":"atypb16","unstructured":"P. Grisvard,\n                      Elliptic Problems in Nonsmooth Domains\n                      , Pitman, Boston, MA, 1985."},{"key":"atypb17","doi-asserted-by":"crossref","unstructured":"D. Holm, T. Schmah, and C. Stoica,\n                      Geometric Mechanics and Symmetry\n                      , Oxford University Press, Oxford, 2009.","DOI":"10.1093\/oso\/9780199212903.001.0001"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1007\/BF01582096"},{"key":"atypb19","doi-asserted-by":"crossref","unstructured":"P. Mehlitz and G. Wachsmuth,\n                      The weak sequential closure of decomposable sets in Lebesgue spaces and its application to variational geometry\n                      , Set-Valued Var. Anal. (2017),https:\/\/doi.org\/10.1007\/s11228-017-0464-1.","DOI":"10.1007\/s11228-017-0464-1"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1016\/0022-1236(76)90017-3"},{"key":"atypb21","doi-asserted-by":"crossref","unstructured":"R. Rockafellar and R. Wets,\n                      Variational Analysis\n                      , Springer, Berlin, 1998.","DOI":"10.1007\/978-3-642-02431-3"},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623495279785"},{"key":"atypb23","unstructured":"G. Wachsmuth,\n                      A guided tour of polyhedric sets: Basic properties, new results on intersections and applications\n                      , J. Convex Anal. (2018),http:\/\/www.heldermann.de\/JCA\/JCA26\/JCA261\/jca26010.htm."},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1007\/BF01442543"}],"container-title":["SIAM Journal on Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/17M1140418","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T19:18:51Z","timestamp":1787339931000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/17M1140418"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,1]]},"references-count":24,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2018,1]]}},"alternative-id":["10.1137\/17M1140418"],"URL":"https:\/\/doi.org\/10.1137\/17m1140418","relation":{},"ISSN":["1052-6234","1095-7189"],"issn-type":[{"value":"1052-6234","type":"print"},{"value":"1095-7189","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,1]]}}}