{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,24]],"date-time":"2025-12-24T03:16:29Z","timestamp":1766546189421,"version":"3.37.3"},"reference-count":17,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2016,7,6]],"date-time":"2016-07-06T00:00:00Z","timestamp":1467763200000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["LO 1379\/7-1"],"award-info":[{"award-number":["LO 1379\/7-1"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Math Meth Oper Res"],"published-print":{"date-parts":[[2016,10]]},"DOI":"10.1007\/s00186-016-0554-0","type":"journal-article","created":{"date-parts":[[2016,7,6]],"date-time":"2016-07-06T01:17:09Z","timestamp":1467767829000},"page":"411-426","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":38,"title":["Equivalence between polyhedral projection, multiple objective linear programming and vector linear programming"],"prefix":"10.1007","volume":"84","author":[{"given":"Andreas","family":"L\u00f6hne","sequence":"first","affiliation":[]},{"given":"Benjamin","family":"Wei\u00dfing","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2016,7,6]]},"reference":[{"key":"554_CR1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1023\/A:1008215702611","volume":"13","author":"H Benson","year":"1998","unstructured":"Benson H (1998) An outer approximation algorithm for generating all efficient extreme points in the outcome set of a multiple objective linear programming problem. J Glob Optim 13:1\u201324","journal-title":"J Glob Optim"},{"issue":"2","key":"554_CR2","doi-asserted-by":"crossref","first-page":"579","DOI":"10.1016\/0022-247X(87)90065-5","volume":"126","author":"JP Dauer","year":"1987","unstructured":"Dauer JP (1987) Analysis of the objective space in multiple objective linear programming. J Math Anal Appl 126(2):579\u2013593","journal-title":"J Math Anal Appl"},{"issue":"3","key":"554_CR3","doi-asserted-by":"crossref","first-page":"350","DOI":"10.1016\/0377-2217(90)90010-9","volume":"46","author":"JP Dauer","year":"1990","unstructured":"Dauer JP, Liu Y-H (1990) Solving multiple objective linear programs in objective space. Eur J Oper Res 46(3):350\u2013357","journal-title":"Eur J Oper Res"},{"issue":"4","key":"554_CR4","doi-asserted-by":"crossref","first-page":"757","DOI":"10.1007\/s10898-011-9709-y","volume":"52","author":"M Ehrgott","year":"2012","unstructured":"Ehrgott M, L\u00f6hne A, Shao L (2012) A dual variant of Benson\u2019s outer approximation algorithm. J Glob Optim 52(4):757\u2013778","journal-title":"J Glob Optim"},{"issue":"5","key":"554_CR5","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1080\/02331887308801134","volume":"4","author":"J Focke","year":"1973","unstructured":"Focke J (1973) Vektormaximumproblem und parametrische Optimierung. Math Operationsforsch Statist 4(5):365\u2013369","journal-title":"Math Operationsforsch Statist"},{"key":"554_CR6","unstructured":"F\u00fcl\u00f6p J (1993) On the equivalence between a linear bilevel programming problem and linear optimization over the efficient set. Technical report, Laboratory of Operations Research and Decision Systems, Computer and Automation Institute, Hungarian Academy of Sciences, Budapest. working paper 93-1"},{"key":"554_CR7","doi-asserted-by":"crossref","unstructured":"Gr\u00fcnbaum B (2003) Convex polytopes, volume 221 of graduate texts in mathematics. 2nd edition. Springer, New York, Prepared by V. Kaibel, V. Klee, and G.M. Ziegler","DOI":"10.1007\/978-1-4613-0019-9"},{"issue":"12","key":"554_CR8","doi-asserted-by":"crossref","first-page":"1421","DOI":"10.1080\/02331931003665108","volume":"60","author":"F Heyde","year":"2011","unstructured":"Heyde F, L\u00f6hne A (2011) Solution concepts in vector optimization: a fresh look at an old story. Optimization 60(12):1421\u20131440","journal-title":"Optimization"},{"issue":"2","key":"554_CR9","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1007\/s10957-008-9384-4","volume":"138","author":"CN Jones","year":"2008","unstructured":"Jones CN, Kerrigan EC, Maciejowski JM (2008) On polyhedral projection and parametric programming. J Optim Theory Appl 138(2):207\u2013220","journal-title":"J Optim Theory Appl"},{"key":"554_CR10","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-18351-5","volume-title":"Vector optimization with infimum and supremum. Vector optimization","author":"A L\u00f6hne","year":"2011","unstructured":"L\u00f6hne A (2011) Vector optimization with infimum and supremum. Vector optimization. Springer, Berlin"},{"key":"554_CR11","doi-asserted-by":"crossref","first-page":"176","DOI":"10.1016\/j.dam.2015.01.030","volume":"186","author":"A L\u00f6hne","year":"2015","unstructured":"L\u00f6hne A, Rudloff B (2015) On the dual of the solvency cone. Discrete Appl Math 186:176\u2013185","journal-title":"Discrete Appl Math"},{"key":"554_CR12","unstructured":"L\u00f6hne A, Wei\u00dfing B (2015) Bensolve-VLP solver, version 2.0.1. http:\/\/bensolve.org"},{"key":"554_CR13","doi-asserted-by":"publisher","unstructured":"L\u00f6hne A, Wei\u00dfing B (2016) The vector linear program solver Bensolve\u2013notes on theoretical background. Eur J Oper Res. doi: 10.1016\/j.ejor.2016.02.039","DOI":"10.1016\/j.ejor.2016.02.039"},{"key":"554_CR14","doi-asserted-by":"crossref","unstructured":"Lotov AV, Bushenkov VA, Kamenev GK (2004) Interactive decision maps, volume 89 applied optimization. Kluwer Academic Publishers, Boston, Approximation and visualization of Pareto frontier. With a foreword by Jared L, Cohon","DOI":"10.1007\/978-1-4419-8851-5"},{"key":"554_CR15","volume-title":"Convex analysis","author":"R Rockafellar","year":"1972","unstructured":"Rockafellar R (1972) Convex analysis. Princeton University Press, Princeton"},{"key":"554_CR16","doi-asserted-by":"crossref","unstructured":"Roux A, Zastawniak T (2015) Set optimization and applications \u2014the state of the art: from set relations to set-valued risk measures, chapter linear vector optimization and European option pricing under proportional transaction costs. Springer, Berlin, pp 159\u2013176","DOI":"10.1007\/978-3-662-48670-2_5"},{"key":"554_CR17","volume-title":"Theory of multiobjective optimization, volume 176 mathematics in science and engineering","author":"Y Sawaragi","year":"1985","unstructured":"Sawaragi Y, Nakayama H, Tanino T (1985) Theory of multiobjective optimization, volume 176 mathematics in science and engineering. Academic Press, Orlando"}],"container-title":["Mathematical Methods of Operations Research"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00186-016-0554-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00186-016-0554-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00186-016-0554-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,10]],"date-time":"2019-09-10T15:28:20Z","timestamp":1568129300000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00186-016-0554-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,7,6]]},"references-count":17,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2016,10]]}},"alternative-id":["554"],"URL":"https:\/\/doi.org\/10.1007\/s00186-016-0554-0","relation":{},"ISSN":["1432-2994","1432-5217"],"issn-type":[{"type":"print","value":"1432-2994"},{"type":"electronic","value":"1432-5217"}],"subject":[],"published":{"date-parts":[[2016,7,6]]}}}