{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,3]],"date-time":"2025-07-03T09:44:32Z","timestamp":1751535872113},"reference-count":18,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[1975,12,1]],"date-time":"1975-12-01T00:00:00Z","timestamp":186624000000},"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":[[1975,12]]},"DOI":"10.1007\/bf01580450","type":"journal-article","created":{"date-parts":[[2005,4,28]],"date-time":"2005-04-28T04:57:06Z","timestamp":1114664226000},"page":"332-344","source":"Crossref","is-referenced-by-count":27,"title":["The theorem of the alternative, the key-theorem, and the vector-maximum problem"],"prefix":"10.1007","volume":"8","author":[{"given":"R.","family":"Lehmann","sequence":"first","affiliation":[]},{"given":"W.","family":"Oettli","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"CR1","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1007\/BF01584093","volume":"1","author":"A. Berman","year":"1971","unstructured":"A. Berman and A. Ben-Israel, \u201cLinear inequalities, mathematical programming and matrix theory\u201d,Mathematical Programming 1 (1971) 291\u2013300.","journal-title":"Mathematical Programming"},{"key":"CR2","doi-asserted-by":"crossref","first-page":"969","DOI":"10.1080\/00029890.1962.11990015","volume":"69","author":"C.C. Braunschweiger","year":"1962","unstructured":"C.C. Braunschweiger, \u201cAn extension of the nonhomogeneous Farkas theorem\u201d,American Mathematical Monthly 69 (1962) 969\u2013975.","journal-title":"American Mathematical Monthly"},{"key":"CR3","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1287\/mnsc.9.2.209","volume":"9","author":"A. Charnes","year":"1963","unstructured":"A. Charnes, W.W. Cooper and K. Kortanek, \u201cDuality in semi-infinite programs and some works of Haar and Carath\u00e9odory\u201d,Management Science 9 (1963) 209\u2013228.","journal-title":"Management Science"},{"key":"CR4","first-page":"157","volume":"38","author":"R.J. Duffin","year":"1956","unstructured":"R.J. Duffin, \u201cInfinite programs\u201d,Annals of Mathematics Studies 38 (1956) 157\u2013170.","journal-title":"Annals of Mathematics Studies"},{"key":"CR5","doi-asserted-by":"crossref","first-page":"122","DOI":"10.1287\/mnsc.12.1.122","volume":"12","author":"R.J. Duffin","year":"1965","unstructured":"R.J. Duffin and L.A. Karlovitz, \u201cAn infinite linear program with a duality gap\u201d,Management Science 12 (1965) 122\u2013134.","journal-title":"Management Science"},{"key":"CR6","unstructured":"J. Focke and A. G\u00f6pfert, \u201c100 Jahre Gordanscher Alternativsatz f\u00fcr lineare Ungleichungen\u201d,Mathematische Operationsforschung und Statistik, to appear."},{"key":"CR7","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1007\/978-3-642-80684-1","volume-title":"Lectures on mathematical theory of extremum problems, Lecture Notes in Economics and Mathematical Systems, 67","author":"I.V. Girsanov","year":"1972","unstructured":"I.V. Girsanov,Lectures on mathematical theory of extremum problems, Lecture Notes in Economics and Mathematical Systems, 67 (Springer, Berlin, 1972) pp. 70\u201371."},{"key":"CR8","first-page":"379","volume-title":"Mathematical models in economics","author":"Ho\u00e0ng Tuy","year":"1974","unstructured":"Ho\u00e0ng Tuy, \u201cThe Farkas\u2014Minkowski theorem and extremum problems, in: J. \u0141o\u015b and M.W. \u0141o\u015b, eds.,Mathematical models in economics (North-Holland, Amsterdam, 1974) pp. 379\u2013400."},{"key":"CR9","doi-asserted-by":"crossref","first-page":"350","DOI":"10.1137\/1013065","volume":"13","author":"C. Kallina","year":"1971","unstructured":"C. Kallina and A.C. Williams, \u201cLinear programming in reflexive spaces\u201d,SIAM Review 13 (1971) 350\u2013376.","journal-title":"SIAM Review"},{"key":"CR10","doi-asserted-by":"crossref","first-page":"320","DOI":"10.1007\/BF01109978","volume":"121","author":"W. Krabs","year":"1971","unstructured":"W. Krabs, \u201cZur Dualit\u00e4tstheorie bei linearen Optimierungsproblemen in halbgeordneten Vektorr\u00e4umen\u201d,Mathematische Zeitschrift 121 (1971) 320\u2013328.","journal-title":"Mathematische Zeitschrift"},{"key":"CR11","doi-asserted-by":"crossref","first-page":"221","DOI":"10.4153\/CJM-1961-019-2","volume":"13","author":"K.S. Kretschmer","year":"1961","unstructured":"K.S. Kretschmer, \u201cProgrammes in paired spaces\u201d,Canadian Journal of Mathematics 13 (1961) 221\u2013238.","journal-title":"Canadian Journal of Mathematics"},{"key":"CR12","first-page":"99","volume":"38","author":"Ky Fan","year":"1956","unstructured":"Ky Fan, \u201cOn systems of linear inequalities\u201d,Annals of Mathematics Studies 38 (1956) 99\u2013156.","journal-title":"Annals of Mathematics Studies"},{"key":"CR13","doi-asserted-by":"crossref","first-page":"152","DOI":"10.1016\/0021-9045(69)90038-0","volume":"2","author":"Ky Fan","year":"1969","unstructured":"Ky Fan, \u201cAsymptotic cones and duality of linear relations\u201d,Journal of Approximation Theory 2 (1969) 152\u2013159.","journal-title":"Journal of Approximation Theory"},{"key":"CR14","first-page":"16","volume-title":"Nonlinear programming","author":"O. Mangasarian","year":"1969","unstructured":"O. Mangasarian,Nonlinear programming (McGraw-Hill, New York, 1969) pp. 16\u201337."},{"key":"CR15","first-page":"33","volume-title":"Convex structures and economic theory","author":"H. Nakaido","year":"1968","unstructured":"H. Nakaido,Convex structures and economic theory (Academic Press, New York, 1968) pp. 33\u201339."},{"key":"CR16","volume-title":"Topological vector spaces","author":"A.P. Robertson","year":"1964","unstructured":"A.P. Robertson and W.J. Robertson,Topological vector spaces (Cambridge University Press, Cambridge, 1964) Chapter II."},{"key":"CR17","volume-title":"Effizienz und Dualit\u00e4t in der Aktivit\u00e4tsanalyse","author":"P. Sch\u00f6nfeld","year":"1964","unstructured":"P. Sch\u00f6nfeld, \u201cEffizienz und Dualit\u00e4t in der Aktivit\u00e4tsanalyse\u201d, Dissertation, Freie Universit\u00e4t Berlin (1964)."},{"key":"CR18","first-page":"99","volume":"74B","author":"C. Witzgall","year":"1970","unstructured":"C. Witzgall, \u201cOn complementary polar conical sets\u201d,Journal of Research of the National Bureau of Standards 74B (1970) 99\u2013113.","journal-title":"Journal of Research of the National Bureau of Standards"}],"container-title":["Mathematical Programming"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF01580450.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/BF01580450\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF01580450","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,3]],"date-time":"2019-05-03T11:12:08Z","timestamp":1556881928000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BF01580450"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1975,12]]},"references-count":18,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1975,12]]}},"alternative-id":["BF01580450"],"URL":"https:\/\/doi.org\/10.1007\/bf01580450","relation":{},"ISSN":["0025-5610","1436-4646"],"issn-type":[{"value":"0025-5610","type":"print"},{"value":"1436-4646","type":"electronic"}],"subject":[],"published":{"date-parts":[[1975,12]]}}}