{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,18]],"date-time":"2026-07-18T11:20:33Z","timestamp":1784373633927,"version":"3.55.0"},"reference-count":7,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[1974,12,1]],"date-time":"1974-12-01T00:00:00Z","timestamp":155088000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Programming"],"published-print":{"date-parts":[[1974,12]]},"DOI":"10.1007\/bf01585523","type":"journal-article","created":{"date-parts":[[2005,4,28]],"date-time":"2005-04-28T09:09:11Z","timestamp":1114679351000},"page":"253-258","source":"Crossref","is-referenced-by-count":28,"title":["Fenchel and Lagrange duality are equivalent"],"prefix":"10.1007","volume":"7","author":[{"given":"T. L.","family":"Magnanti","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","reference":[{"key":"CR1","doi-asserted-by":"crossref","first-page":"617","DOI":"10.1090\/S0002-9939-1957-0087574-2","volume":"8","author":"Ky Fan","year":"1957","unstructured":"Ky Fan, I. Glicksberg and A.J. Hoffman, \u201cSystems of inequalities involving convex functions\u201d,Proceedings of the American Mathematical Society 8 (1957) 617\u2013622.","journal-title":"Proceedings of the American Mathematical Society"},{"key":"CR2","volume-title":"\u201cConvex cones, sets and functions\u201d, lecture notes","author":"W. Fenchel","year":"1951","unstructured":"W. Fenchel, \u201cConvex cones, sets and functions\u201d, lecture notes, Princeton University, Princeton, N.J. (1951)."},{"key":"CR3","volume-title":"Optimization by vector space methods","author":"D. Luenberger","year":"1969","unstructured":"D. Luenberger,Optimization by vector space methods (Wiley, New York, 1969)."},{"key":"CR4","unstructured":"T.L. Magnanti, \u201cA linear approximation approach to duality in nonlinear programming\u201d, Tech. Rept. OR 016-73, Operations Research Center, M.I.T. (April 1973)."},{"key":"CR5","doi-asserted-by":"crossref","DOI":"10.1515\/9781400873173","volume-title":"Convex analysis","author":"R.T. Rockafellar","year":"1970","unstructured":"R.T. Rockafellar,Convex analysis (Princeton University Press, Princeton, N.J., 1970)."},{"key":"CR6","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":"J. Stoer and C. Witzgall,Convexity and optimization in finite dimensions I (Springer, Berlin, 1970)."},{"key":"CR7","first-page":"77","volume-title":"Nonlinear programming","author":"A. Whinston","year":"1967","unstructured":"A. Whinston, \u201cSome applications of the conjugate function theory to duality\u201d, in: J. Abadie, ed.,Nonlinear programming (North-Holland, Amsterdam, 1967) pp. 77\u201398."}],"container-title":["Mathematical Programming"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF01585523.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/BF01585523\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF01585523","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,3]],"date-time":"2019-05-03T15:32:28Z","timestamp":1556897548000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BF01585523"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1974,12]]},"references-count":7,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1974,12]]}},"alternative-id":["BF01585523"],"URL":"https:\/\/doi.org\/10.1007\/bf01585523","relation":{},"ISSN":["0025-5610","1436-4646"],"issn-type":[{"value":"0025-5610","type":"print"},{"value":"1436-4646","type":"electronic"}],"subject":[],"published":{"date-parts":[[1974,12]]}}}