{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,23]],"date-time":"2026-02-23T17:33:52Z","timestamp":1771868032527,"version":"3.50.1"},"reference-count":24,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[1982,12,1]],"date-time":"1982-12-01T00:00:00Z","timestamp":407548800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Zeitschrift f\u00fcr Operations Research"],"published-print":{"date-parts":[[1982,12]]},"DOI":"10.1007\/bf01917114","type":"journal-article","created":{"date-parts":[[2005,7,30]],"date-time":"2005-07-30T12:34:17Z","timestamp":1122726857000},"page":"197-209","source":"Crossref","is-referenced-by-count":3,"title":["On abstract duality in mathematical programming"],"prefix":"10.1007","volume":"26","author":[{"given":"R. E.","family":"Burkard","sequence":"first","affiliation":[]},{"given":"H.","family":"Hamacher","sequence":"additional","affiliation":[]},{"given":"J.","family":"Tind","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"BF01917114_CR1","unstructured":"Ben-Tal, A., andA. Ben-Israel:F-convex Functions: Properties and Applications. Generalised Concavity in Optimization and Economics. Ed. by S. Schaible and W.C. Ziemba. New York 1981, 301\u2013334."},{"key":"BF01917114_CR2","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1007\/BF01583794","volume":"23","author":"C.E. Blair","year":"1982","unstructured":"Blair, C.E., andR.G. Jeroslow: The Value Function of an Integer Program. Mathematical Programming23, 1982, 237\u2013273.","journal-title":"Mathematical Programming"},{"key":"BF01917114_CR3","unstructured":"Burkard, R.E., andU. Zimmermann: Combinatorial Optimization in Linearly Ordered Semimodules: A Survey. Modern Applied Mathematics: Optimization and Operations Research. Ed. by B. Korte. Amsterdam 1982, 391\u2013436."},{"key":"BF01917114_CR4","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1137\/0316018","volume":"16","author":"S. Dolecki","year":"1978","unstructured":"Dolecki, S., andS. Kurcyusz: On \u03a6-Convexity in Extremal Problems. SIAM Journal on Control and Optimization16, 1978, 277\u2013300.","journal-title":"SIAM Journal on Control and Optimization"},{"key":"BF01917114_CR5","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1080\/02331887408801144","volume":"5","author":"K.H. Elster","year":"1974","unstructured":"Elster, K.H., andR. Nehse: Zur Theorie der Polarfunktionale. Mathematische Operationsforschung und Statistik5, 1974, 3\u201321.","journal-title":"Mathematische Operationsforschung und Statistik"},{"key":"BF01917114_CR6","doi-asserted-by":"crossref","first-page":"399","DOI":"10.1287\/opre.11.3.399","volume":"11","author":"H. Everett","year":"1963","unstructured":"Everett, H.: Generalized Lagrange Multiplier Method for Solving Problems of Optimum Allocation of Resources. Operations Research11, 1963, 399\u2013417.","journal-title":"Operations Research"},{"key":"BF01917114_CR7","volume-title":"Memorandum No 336","author":"J.M.M. Evers","year":"1981","unstructured":"Evers, J.M.M., andH. van Maaren: Duality Principles in Mathematics and Their Relations to Conjugate Functions. Memorandum No 336, Department of Applied Mathematics, Twente University of Technology, Enschede 1981."},{"key":"BF01917114_CR8","doi-asserted-by":"crossref","first-page":"1280","DOI":"10.1137\/0117120","volume":"17","author":"F.J. Gould","year":"1969","unstructured":"Gould, F.J.: Extensions of Lagrange Multipliers in Nonlinear Programming. SIAM Journal on Applied Mathematics17, 1969, 1280\u20131297.","journal-title":"SIAM Journal on Applied Mathematics"},{"key":"BF01917114_CR9","first-page":"196","volume":"14","author":"F.J. Gould","year":"1972","unstructured":"\u2014: Nonlinear Duality Theorems. Cahiers du Centre d'Etudes de Recherche Op\u00e9rationelle14, 1972, 196\u2013212.","journal-title":"Cahiers du Centre d'Etudes de Recherche Op\u00e9rationelle"},{"key":"BF01917114_CR10","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1002\/nav.3800100131","volume":"10","author":"A.J. Hoffman","year":"1963","unstructured":"Hoffman, A.J.: On Abstract Dual Linear Programs. Naval Research Logistics Quarterly10, 1963, 369\u2013373.","journal-title":"Naval Research Logistics Quarterly"},{"key":"BF01917114_CR11","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1016\/0012-365X(78)90112-7","volume":"23","author":"R.G. Jeroslow","year":"1978","unstructured":"Jeroslow, R.G.: Cutting Plane Theory: Algebraic Methods. Discrete Mathematics23, 1978, 121\u2013150.","journal-title":"Discrete Mathematics"},{"key":"BF01917114_CR12","doi-asserted-by":"crossref","unstructured":"Johnson, E.L.: Cyclic Groups, Cutting Planes and Shortest Paths. Mathematical Programming. Ed. by T.C. Hu and S. Robinson. New York 1973, 185\u2013211.","DOI":"10.1016\/B978-0-12-358350-5.50009-9"},{"key":"BF01917114_CR13","doi-asserted-by":"crossref","first-page":"212","DOI":"10.1007\/BF01580392","volume":"11","author":"T.C. Koopmans","year":"1976","unstructured":"Koopmans, T.C.: Concepts of Optimality and Their Uses. Nobel Memorial Lecture, December 1975. Mathematical Programming11, 1976, 212\u2013228.","journal-title":"Mathematical Programming"},{"key":"BF01917114_CR14","unstructured":"Luce, R.D., andH. Raiffa: Games and Decisions. New York 1957."},{"key":"BF01917114_CR15","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1007\/BF01585518","volume":"7","author":"R.R. Meyer","year":"1974","unstructured":"Meyer, R.R.. On the Existence of Optimal Solutions to Integer and Mixed Integer Programming Problems. Mathematical Programming7, 1974, 223\u2013235.","journal-title":"Mathematical Programming"},{"key":"BF01917114_CR16","doi-asserted-by":"crossref","unstructured":"Rockafellar, R.T.: Convex Analysis. Princeton, 1970.","DOI":"10.1515\/9781400873173"},{"key":"BF01917114_CR17","doi-asserted-by":"crossref","first-page":"268","DOI":"10.1137\/0312021","volume":"12","author":"R.T. Rockafellar","year":"1974","unstructured":"\u2014: Augmented Lagrange Multiplier Functions and Duality in Nonconvex Programming. SIAM Journal on Control12, 1974, 268\u2013283.","journal-title":"SIAM Journal on Control"},{"key":"BF01917114_CR18","first-page":"193","volume":"32","author":"J. Tind","year":"1979","unstructured":"Tind, J.: On Duality in Nonconvex and Integer Programming. Operations Research Verfahren32, 1979, 193\u2013201.","journal-title":"Operations Research Verfahren"},{"key":"BF01917114_CR19","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1007\/BF01584248","volume":"21","author":"J. Tind","year":"1981","unstructured":"Tind, J., andL.A. Wolsey: An Elementary Survey of General Duality Theory in Mathematical Programming. Mathematical Programming21, 1981, 241\u2013261.","journal-title":"Mathematical Programming"},{"key":"BF01917114_CR20","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1007\/BF01589344","volume":"20","author":"L.A. Wolsey","year":"1981","unstructured":"Wolsey, L.A.: Integer Programming Duality: Price Functions and Sensitivity Analysis. Mathematical Programming20, 1981, 173\u2013194.","journal-title":"Mathematical Programming"},{"key":"BF01917114_CR21","first-page":"428","volume":"10","author":"K. Zimmermann","year":"1974","unstructured":"Zimmermann, K.: Conjugate Optimization Problems and Algorithms in the Extremal Vector Space. Ekonomicko-mathematick\u00fd obzor10, 1974, 428\u2013439.","journal-title":"Ekonomicko-mathematick\u00fd obzor"},{"key":"BF01917114_CR22","first-page":"438","volume":"15","author":"U. Zimmermann","year":"1979","unstructured":"Zimmermann, U.: On Some Extremal Optimization Problems. Ekonomicko-mathematick\u00fd obzor15, 1979, 438\u2013442.","journal-title":"Ekonomicko-mathematick\u00fd obzor"},{"key":"BF01917114_CR23","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1016\/0024-3795(80)90004-X","volume":"32","author":"U. Zimmermann","year":"1980","unstructured":"\u2014: Duality for Algebraic Linear Programming. Linear Algebra and Its Applications32, 1980, 9\u201331.","journal-title":"Linear Algebra and Its Applications"},{"key":"BF01917114_CR24","unstructured":"-: Linear and Combinatorial Optimization in Ordered Algebraic Structures. Annals of Discrete Mathematics 10. Amsterdam 1981."}],"container-title":["Zeitschrift f\u00fcr Operations Research"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF01917114.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/BF01917114\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF01917114","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,4,8]],"date-time":"2020-04-08T12:49:17Z","timestamp":1586350157000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BF01917114"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1982,12]]},"references-count":24,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1982,12]]}},"alternative-id":["BF01917114"],"URL":"https:\/\/doi.org\/10.1007\/bf01917114","relation":{},"ISSN":["0340-9422","1432-5217"],"issn-type":[{"value":"0340-9422","type":"print"},{"value":"1432-5217","type":"electronic"}],"subject":[],"published":{"date-parts":[[1982,12]]}}}