{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,7,24]],"date-time":"2024-07-24T13:10:43Z","timestamp":1721826643851},"reference-count":26,"publisher":"Springer Science and Business Media LLC","issue":"1-3","license":[{"start":{"date-parts":[[1988,5,1]],"date-time":"1988-05-01T00:00:00Z","timestamp":578448000000},"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":[[1988,5]]},"DOI":"10.1007\/bf01580766","type":"journal-article","created":{"date-parts":[[2005,4,28]],"date-time":"2005-04-28T05:52:50Z","timestamp":1114667570000},"page":"249-260","source":"Crossref","is-referenced-by-count":26,"title":["A note on the solution of bilinear programming problems by reduction to concave minimization"],"prefix":"10.1007","volume":"41","author":[{"given":"Tran Vu","family":"Thieu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"CR1","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1287\/moor.8.2.273","volume":"8","author":"F. Al-Khayyal","year":"1983","unstructured":"F. Al-Khayyal and J.E. Falk, \u201cJointly constrained biconvex programming,\u201dMathematics of Operations Research 8 (1983) 273\u2013286.","journal-title":"Mathematics of Operations Research"},{"key":"CR2","first-page":"741","volume":"16","author":"M. Altman","year":"1968","unstructured":"M. Altman, \u201cBilinear Programming,\u201dBulletin de l'Academie Polonaise des Sciences, 16 (1968) 741\u2013746.","journal-title":"Bulletin de l'Academie Polonaise des Sciences"},{"key":"CR3","unstructured":"V.T. Ban, \u201cA Finite Algorithm for Globally Minimizing a Concave Function under Linear Constraints and its Applications,\u201d Proceedings of IFIP Working Conference on Recent Advances on System Modelling and Optimization, Hanoi, January 1983."},{"key":"CR4","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1002\/nav.3800320119","volume":"32","author":"H.P. Benson","year":"1985","unstructured":"H.P. Benson, \u201cA finite algorithm for concave minimization over a polyhedron,\u201dNaval Research Logistics Quarterly 32 (1985) 165\u2013177.","journal-title":"Naval Research Logistics Quarterly"},{"key":"CR5","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1007\/BF01580119","volume":"5","author":"J.E. Falk","year":"1973","unstructured":"J.E. Falk, \u201cA linear max-min problem,\u201dMathematical Programming 5 (1973) 169\u2013188.","journal-title":"Mathematical Programming"},{"key":"CR6","doi-asserted-by":"crossref","first-page":"376","DOI":"10.1007\/BF01585532","volume":"7","author":"A.M. Frieze","year":"1974","unstructured":"A.M. Frieze, \u201cA bilinear programming formulation of the 3-dimensional assignment problem,\u201dMathematical Programming 7 (1974) 376\u2013379.","journal-title":"Mathematical Programming"},{"key":"CR7","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1007\/BF01593787","volume":"12","author":"G. Gallo","year":"1977","unstructured":"G. Gallo and A. Ulk\u00fcc\u00fc, \u201cBilinear programming: An exact algorithm,\u201dMathematical Programming 12 (1977) 173\u2013194.","journal-title":"Mathematical Programming"},{"key":"CR8","unstructured":"H. Konno, \u201cBilinear programming Part II: Applications of bilinear programming,\u201d Technical Report 71-10, Dept. of OR, Stanford University (1971)."},{"key":"CR9","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1007\/BF01580367","volume":"11","author":"H. Konno","year":"1976","unstructured":"H. Konno, \u201cA cutting plane algorithm for solving bilinear programs,\u201dMathematical Programming 11 (1976) 14\u201327.","journal-title":"Mathematical Programming"},{"key":"CR10","first-page":"778","volume":"12","author":"O.L. Mangasarian","year":"1964","unstructured":"O.L. Mangasarian, \u201cEquilibrium points of bimatrix games,\u201dSIAM Journal 12 (1964) 778\u2013780.","journal-title":"SIAM Journal"},{"key":"CR11","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1016\/0022-247X(64)90021-6","volume":"9","author":"O.L. Mangasarian","year":"1964","unstructured":"O.L. Mangasarian and H. Stone, \u201cTwo person nonzero-sum games and quadratic programming,\u201dJournal of Mathematical Analysis and Applications 9 (1964) 345\u2013355.","journal-title":"Journal of Mathematical Analysis and Applications"},{"key":"CR12","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, NJ, 1970)."},{"key":"CR13","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1007\/BF01581626","volume":"19","author":"H.D. Sherali","year":"1980","unstructured":"H.D. Sherali and C.M. Shetty, \u201cA finitely convergent algorithm for bilinear programming problems using polar cuts and disjunctive face cuts,\u201dMathematical Programming 19 (1980) 14\u201331.","journal-title":"Mathematical Programming"},{"key":"CR14","volume-title":"\u201cRectilinear distance location-allocation problem: A simplex based algorithm,\u201d Proceedings of the International Symposium on Extreme Methods and Systems Analysis","author":"C.M. Shetty","year":"1980","unstructured":"C.M. Shetty and H.D. Sherali, \u201cRectilinear distance location-allocation problem: A simplex based algorithm,\u201d Proceedings of the International Symposium on Extreme Methods and Systems Analysis, Lecture Notes in Economics and Mathematical Systems (Springer, Berlin, 1980)."},{"key":"CR15","first-page":"106","volume":"4","author":"E.N. Sokirjanskaja","year":"1974","unstructured":"E.N. Sokirjanskaja, \u201cNekotorye algoritmy bilineinovo programmirovanija,\u201dKibernetika 4 (1974) 106\u2013112.","journal-title":"Kibernetika"},{"key":"CR16","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1287\/opre.22.2.373","volume":"22","author":"R.M. Soland","year":"1974","unstructured":"R.M. Soland, \u201cOptimal facility location with concave costs,\u201dOperations Research 22 (1974) 373\u2013382.","journal-title":"Operations Research"},{"key":"CR17","first-page":"106","volume":"5","author":"T.V. Thieu","year":"1980","unstructured":"T.V. Thieu, \u201cRelationship between bilinear programming and concave minimization under linear constraints,\u201dActa Mathematica Vietnamica 5 (1980) 106\u2013113.","journal-title":"Acta Mathematica Vietnamica"},{"key":"CR18","volume-title":"\u201cComputer program for concave minimization over a polytope,\u201d Preprint No. 18","author":"T.V. Thieu","year":"1983","unstructured":"T.V. Thieu, \u201cComputer program for concave minimization over a polytope,\u201d Preprint No. 18, Institute of Mathematics, Hanoi 1983."},{"key":"CR19","first-page":"173","volume":"9","author":"T.V. Thieu","year":"1984","unstructured":"T.V. Thieu, \u201cA finite method for globally minimizing concave functions over unbounded polyhedral convex sets and its applications,\u201dActa Mathematica Vietnamica 9 (1984) 173\u2013191.","journal-title":"Acta Mathematica Vietnamica"},{"key":"CR20","first-page":"21","volume":"8","author":"T.V. Thieu","year":"1983","unstructured":"T.V. Thieu, B.T. Tam and V.T. Ban, \u201cAn outer approximation method for globally minimizing a concave function over a compact convex set,\u201dActa Mathematica Vietnamica, 8 (1983) 21\u201340.","journal-title":"Acta Mathematica Vietnamica"},{"key":"CR21","first-page":"32","volume":"159","author":"H. Tuy","year":"1964","unstructured":"H. Tuy, \u201cConcave programming under linear constraints,\u201dDoklady Akademiia Nauk USSR 159 (1964), 32\u201335. Translated inSoviet Mathematics Doklady 5 (1964) 1437\u20131440.","journal-title":"Doklady Akademiia Nauk USSR"},{"key":"CR22","unstructured":"H. Tuy, \u201cGlobal maximization of a convex function over a closed, convex, not necessarily bounded set,\u201d Cahier de Math. de la Decision No. 8223 CEREMADE Universit\u00e9 Paris-Dauphine (1982)."},{"key":"CR23","first-page":"3","volume":"8","author":"H. Tuy","year":"1983","unstructured":"H. Tuy, \u201cOn outer approximation methods for solving concave minimization problems,\u201dActa Mathematica Vietnamica 8 (1983) 3\u201334.","journal-title":"Acta Mathematica Vietnamica"},{"key":"CR24","doi-asserted-by":"crossref","first-page":"498","DOI":"10.1287\/moor.10.3.498","volume":"10","author":"H. Tuy","year":"1985","unstructured":"H. Tuy, T.V. Thieu and Ng.Q. Thai, \u201cA conical algorithm for globally minimizing a concave function over a closed convex set,\u201dMathematics of Operations Research 10 (1985) 498\u2013514.","journal-title":"Mathematics of Operations Research"},{"key":"CR25","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1002\/nav.3800230212","volume":"23","author":"H. Vaish","year":"1976","unstructured":"H. Vaish and C.M. Shetty, \u201cThe bilinear programming problem,\u201dNaval Research Logistics Quarterly 23 (1976) 303\u2013309.","journal-title":"Naval Research Logistics Quarterly"},{"key":"CR26","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1002\/nav.3800240107","volume":"24","author":"H. Vaish","year":"1977","unstructured":"H. Vaish and C.M. Shetty, \u201cA cutting plane algorithm for the bilinear programming problem,\u201dNaval Research Logistics Quarterly 24 (1977) 83\u201394.","journal-title":"Naval Research Logistics Quarterly"}],"container-title":["Mathematical Programming"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF01580766.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/BF01580766\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF01580766","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,3]],"date-time":"2019-05-03T11:12:11Z","timestamp":1556881931000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BF01580766"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1988,5]]},"references-count":26,"journal-issue":{"issue":"1-3","published-print":{"date-parts":[[1988,5]]}},"alternative-id":["BF01580766"],"URL":"https:\/\/doi.org\/10.1007\/bf01580766","relation":{},"ISSN":["0025-5610","1436-4646"],"issn-type":[{"value":"0025-5610","type":"print"},{"value":"1436-4646","type":"electronic"}],"subject":[],"published":{"date-parts":[[1988,5]]}}}