{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,7]],"date-time":"2025-07-07T09:26:17Z","timestamp":1751880377597,"version":"3.41.0"},"reference-count":17,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[1998,12,1]],"date-time":"1998-12-01T00:00:00Z","timestamp":912470400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[1998,12,1]],"date-time":"1998-12-01T00:00:00Z","timestamp":912470400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Global Optimization"],"published-print":{"date-parts":[[1998,12]]},"DOI":"10.1023\/a:1008300205223","type":"journal-article","created":{"date-parts":[[2002,12,22]],"date-time":"2002-12-22T14:41:38Z","timestamp":1040568098000},"page":"337-347","source":"Crossref","is-referenced-by-count":15,"title":["Conjugate Functions for Convex and Nonconvex Duality"],"prefix":"10.1007","volume":"13","author":[{"given":"Werner","family":"Oettli","sequence":"first","affiliation":[]},{"given":"Dirk","family":"Schl\u00e4ger","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"186353_CR1","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1137\/0315022","volume":"15","author":"E. J. Balder","year":"1977","unstructured":"Balder, E. J. (1977), An extension of duality-stability relations to nonconvex optimization problems, SIAM Journal of Control and Optimization 15: 329\u2013343.","journal-title":"SIAM Journal of Control and Optimization"},{"key":"186353_CR2","doi-asserted-by":"crossref","first-page":"463","DOI":"10.4153\/CMB-1992-061-7","volume":"35","author":"J. M. Borwein","year":"1992","unstructured":"Borwein, J. M. and Th\u00e9ra, M. (1992), Sandwich theorems for semicontinuous operators, Canadian Mathematical Bulletin 35: 463\u2013474.","journal-title":"Canadian Mathematical Bulletin"},{"key":"186353_CR3","volume-title":"Analyse fonctionnelle","author":"H. Br\u00e9zis","year":"1987","unstructured":"Br\u00e9zis, H. (1987), Analyse fonctionnelle, Masson, Paris."},{"key":"186353_CR4","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1137\/0316018","volume":"16","author":"S. Dolecki","year":"1978","unstructured":"Dolecki, S. and Kurcyusz, S. (1978), On \u0424-convexity in extremal problems, SIAM Journal of Control and Optimization 16: 277\u2013300.","journal-title":"SIAM Journal of Control and Optimization"},{"key":"186353_CR5","volume-title":"Convex Analysis and Variational Problems","author":"I. Ekeland","year":"1976","unstructured":"Ekeland, I. and Temam, R. (1976), Convex Analysis and Variational Problems, North-Holland, Amsterdam."},{"key":"186353_CR6","volume-title":"General Topology, Revised and Completed Edition","author":"R. Engelking","year":"1989","unstructured":"Engelking, R. (1989), General Topology, Revised and Completed Edition, Heldermann, Berlin."},{"key":"186353_CR7","doi-asserted-by":"crossref","first-page":"73","DOI":"10.4153\/CJM-1949-007-x","volume":"1","author":"W. Fenchel","year":"1949","unstructured":"Fenchel, W. (1949), On conjugate convex functions, Canadian Journal of Mathematics 1: 73\u201377.","journal-title":"Canadian Journal of Mathematics"},{"key":"186353_CR8","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1080\/02331939508844059","volume":"33","author":"F. Flores-Baz\u00e1n","year":"1995","unstructured":"Flores-Baz\u00e1n, F. (1995), On a notion of subdifferentiability for non-convex functions, Optimization 33: 1\u20138.","journal-title":"Optimization"},{"key":"186353_CR9","first-page":"91","volume":"126","author":"H. Hahn","year":"1917","unstructured":"Hahn, H. (1917), \u00d1ber halbstetige und unstetige Funktionen, Sitzungsberichte Akad. Wiss. Wien Abt. IIa 126: 91\u2013110.","journal-title":"Sitzungsberichte Akad. Wiss. Wien Abt. IIa"},{"key":"186353_CR10","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1007\/978-1-4757-6019-4_13","volume-title":"Nonsmooth Optimization and Related Topics","author":"J.-B. Hiriart-Urruty","year":"1989","unstructured":"Hiriart-Urruty, J.-B. (1989), From convex optimization to nonconvex optimization. Necessary and sufficient conditions for global optimality, in: F. H. Clarke, V. F. Demyanov, F. Giannessi (eds.), Nonsmooth Optimization and Related Topics, pp. 219\u2013239, Plenum, New York."},{"key":"186353_CR11","first-page":"109","volume":"49","author":"J. J. Moreau","year":"1970","unstructured":"Moreau, J. J. (1970), Inf-convolution, sous-additivit\u00e9, convexit\u00e9 des fonctions num\u00e9riques, Journal de Math\u00e9matiques Pures et Appliqu\u00e9es 49: 109\u2013154.","journal-title":"Journal de Math\u00e9matiques Pures et Appliqu\u00e9es"},{"key":"186353_CR12","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1007\/BF01720979","volume":"17","author":"W. Oettli","year":"1995","unstructured":"Oettli, W. (1995), Kolmogorov conditions for vectorial optimization problems, OR Spektrum 17: 227\u2013229.","journal-title":"OR Spektrum"},{"key":"186353_CR13","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-017-1588-1","volume-title":"Foundations of Mathematical Optimization","author":"D. Pallaschke","year":"1997","unstructured":"Pallaschke, D. and Rolewicz, S. (1997), Foundations of Mathematical Optimization, Kluwer Academic Publishers, Dordrecht\/Boston\/London."},{"key":"186353_CR14","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611970524","volume-title":"Conjugate Duality and Optimization","author":"R. T. Rockafellar","year":"1974","unstructured":"Rockafellar, R. T. (1974), Conjugate Duality and Optimization, Society for Industrial and Applied Mathematics, Philadelphia."},{"key":"186353_CR15","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-46216-0","volume-title":"Convexity and Optimization in Finite Dimensions I","author":"J. Stoer","year":"1970","unstructured":"Stoer, J. and Witzgall, C. (1970), Convexity and Optimization in Finite Dimensions I, Springer Verlag, Berlin."},{"key":"186353_CR16","volume-title":"An Introduction to Classical Real Analysis","author":"K. R. Stromberg","year":"1981","unstructured":"Stromberg, K. R. (1981), An Introduction to Classical Real Analysis, Wadsworth International, Belmont."},{"key":"186353_CR17","first-page":"39","volume":"15","author":"H. Tuy","year":"1994","unstructured":"Tuy, H. and Oettli, W. (1994), On necessary and sufficient conditions for global optimality, Revista de Matem\u00e1ticas Aplicadas 15: 39\u201341.","journal-title":"Revista de Matem\u00e1ticas Aplicadas"}],"container-title":["Journal of Global Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1008300205223.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1023\/A:1008300205223\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1008300205223.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,1]],"date-time":"2025-07-01T10:39:30Z","timestamp":1751366370000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1023\/A:1008300205223"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,12]]},"references-count":17,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1998,12]]}},"alternative-id":["186353"],"URL":"https:\/\/doi.org\/10.1023\/a:1008300205223","relation":{},"ISSN":["0925-5001","1573-2916"],"issn-type":[{"type":"print","value":"0925-5001"},{"type":"electronic","value":"1573-2916"}],"subject":[],"published":{"date-parts":[[1998,12]]}}}