{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,12]],"date-time":"2026-06-12T13:45:49Z","timestamp":1781271949498,"version":"3.54.1"},"reference-count":24,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2014,1,12]],"date-time":"2014-01-12T00:00:00Z","timestamp":1389484800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Glob Optim"],"published-print":{"date-parts":[[2014,12]]},"DOI":"10.1007\/s10898-013-0136-0","type":"journal-article","created":{"date-parts":[[2014,1,11]],"date-time":"2014-01-11T08:28:46Z","timestamp":1389428926000},"page":"713-736","source":"Crossref","is-referenced-by-count":52,"title":["Primal and dual approximation algorithms for convex vector optimization problems"],"prefix":"10.1007","volume":"60","author":[{"given":"Andreas","family":"L\u00f6hne","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Birgit","family":"Rudloff","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Firdevs","family":"Ulus","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2014,1,12]]},"reference":[{"key":"136_CR1","unstructured":"Ararat, \u00c7, Hamel, A.H., Rudloff, B.: Set-valued shortfall and divergence risk measures. submitted (2013)"},{"key":"136_CR2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1023\/A:1008215702611","volume":"13","author":"HP Benson","year":"1998","unstructured":"Benson, H.P.: 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 (1998)","journal-title":"J. Glob. Optim."},{"issue":"3","key":"136_CR3","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1007\/PL00009389","volume":"20","author":"D Bremner","year":"1998","unstructured":"Bremner, D., Fukuda, K., Marzetta, A.: Primal-dual methods for vertex and facet enumeration. Discrete Comput. Geom. 20(3), 333\u2013357 (1998)","journal-title":"Discrete Comput. Geom."},{"key":"136_CR4","unstructured":"Csirmaz L.: Using multiobjective optimization to map the entropy region of four random variables. Preprint http:\/\/eprints.renyi.hu\/66\/2\/globopt.pdf (2013)"},{"key":"136_CR5","unstructured":"CVX Research. Inc.: CVX: Matlab software for disciplined convex programming, version 2.0 beta., September 2012"},{"issue":"4","key":"136_CR6","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.: A dual variant of Benson\u2019s outer approximation algorithm. J. Glob. Optim. 52(4), 757\u2013778 (2012)","journal-title":"J. Glob. Optim."},{"issue":"3","key":"136_CR7","doi-asserted-by":"crossref","first-page":"397","DOI":"10.1007\/s10898-010-9588-7","volume":"50","author":"M Ehrgott","year":"2011","unstructured":"Ehrgott, M., Shao, L., Sch\u00f6bel, A.: An approximation algorithm for convex multi-objective programming problems. J. Glob. Optim. 50(3), 397\u2013416 (2011)","journal-title":"J. Glob. Optim."},{"key":"136_CR8","doi-asserted-by":"crossref","unstructured":"Ehrgott, M., Wiecek, M. M.: Multiobjective Programming. In: Figueira, J., Greco, S., Ehrgott, M., (eds.) Multiple Criteria Decision Analysis: State of the Art Surveys. Springer Science + Business Media, Berlin, pp. 667\u2013722 (2005)","DOI":"10.1007\/0-387-23081-5_17"},{"key":"136_CR9","doi-asserted-by":"crossref","unstructured":"Grant, M., Boyd, S.: Recent advances in learning and control, chapter Graph implementations for nonsmooth convex programs. Lecture Notes in Control and Information Sciences. Springer, Berlin, pp. 95\u2013110 (2008)","DOI":"10.1007\/978-1-84800-155-8_7"},{"key":"136_CR10","author":"AH Hamel","year":"2013","unstructured":"Hamel, A.H., L\u00f6hne, A.: Lagrange duality in set optimization. J. Optim. Theory Appl. (2013). doi: 10.1007\/s10957-013-0431-4","journal-title":"J. Optim. Theory Appl."},{"key":"136_CR11","author":"AH Hamel","year":"2013","unstructured":"Hamel, A.H., L\u00f6hne, A., Rudloff, B.: A Benson type algorithm for linear vector optimization and applications. J. Glob. Optim. (2013). doi: 10.1007\/s10898-013-0098-2","journal-title":"J. Glob. Optim."},{"issue":"2","key":"136_CR12","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1007\/s11579-013-0094-9","volume":"7","author":"AH Hamel","year":"2013","unstructured":"Hamel, A.H., Rudloff, B., Yankova, M.: Set-valued average value at risk and its computation. Math. Financ. Econ. 7(2), 229\u2013246 (2013)","journal-title":"Math. Financ. Econ."},{"issue":"3","key":"136_CR13","first-page":"813","volume":"20","author":"F Heyde","year":"2013","unstructured":"Heyde, F.: Geometric duality for convex vector optimization problems. J. Convex Anal. 20(3), 813\u2013832 (2013)","journal-title":"J. Convex Anal."},{"issue":"2","key":"136_CR14","doi-asserted-by":"crossref","first-page":"836","DOI":"10.1137\/060674831","volume":"19","author":"F Heyde","year":"2008","unstructured":"Heyde, F., L\u00f6hne, A.: Geometric duality in multiple objective linear programming. SIAM J. Optim. 19(2), 836\u2013845 (2008)","journal-title":"SIAM J. Optim."},{"issue":"12","key":"136_CR15","doi-asserted-by":"crossref","first-page":"1421","DOI":"10.1080\/02331931003665108","volume":"60","author":"F Heyde","year":"2011","unstructured":"Heyde, F., L\u00f6hne, A.: Solution concepts in vector optimization: a fresh look at an old story. Optimization 60(12), 1421\u20131440 (2011)","journal-title":"Optimization"},{"key":"136_CR16","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-540-24828-6","volume-title":"Vector Optimization: Theory, Applications, and Extensions","author":"J Jahn","year":"2004","unstructured":"Jahn, J.: Vector Optimization: Theory, Applications, and Extensions. Springer, Berlin (2004)"},{"key":"136_CR17","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1007\/s007800050061","volume":"3","author":"YM Kabanov","year":"1999","unstructured":"Kabanov, Y.M.: Hedging and liquidation under transaction costs in currency markets. Financ. Stoch. 3, 237\u2013248 (1999)","journal-title":"Financ. Stoch."},{"key":"136_CR18","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-18351-5","volume-title":"Vector Optimization with Infimum and Supremum","author":"A L\u00f6hne","year":"2011","unstructured":"L\u00f6hne, A.: Vector Optimization with Infimum and Supremum. Springer, Berlin (2011)"},{"key":"136_CR19","unstructured":"L\u00f6hne, A., Rudloff, B.: An algorithm for calculating the set of superhedging portfolios in markets with transaction costs. Int. J. Theor. Appl. Finance. (to appear)"},{"key":"136_CR20","doi-asserted-by":"crossref","unstructured":"Luc, D.: Theory of vector optimization. In: Lecture Notes in Economics and Mathematical Systems, vol. 319. Springer, Berlin (1989)","DOI":"10.1007\/978-3-642-50280-4"},{"key":"136_CR21","doi-asserted-by":"crossref","DOI":"10.1515\/9781400873173","volume-title":"Convex Analysis","author":"RT Rockafellar","year":"1970","unstructured":"Rockafellar, R.T.: Convex Analysis. Princeton University Press, Princeton (1970)"},{"issue":"3","key":"136_CR22","doi-asserted-by":"crossref","first-page":"473","DOI":"10.1007\/s10957-005-5494-4","volume":"126","author":"S Ruzika","year":"2005","unstructured":"Ruzika, S., Wiecek, M.M.: Approximation methods in multiobjective programming. J. Optim. Theory Appl. 126(3), 473\u2013501 (2005)","journal-title":"J. Optim. Theory Appl."},{"issue":"2","key":"136_CR23","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1007\/s00186-008-0220-2","volume":"68","author":"L Shao","year":"2008","unstructured":"Shao, L., Ehrgott, M.: Approximately solving multiobjective linear programmes in objective space and an application in radiotherapy treatment planning. Math. Methods Oper. Res. 68(2), 257\u2013276 (2008)","journal-title":"Math. Methods Oper. Res."},{"issue":"3","key":"136_CR24","doi-asserted-by":"crossref","first-page":"469","DOI":"10.1007\/s00186-007-0194-5","volume":"68","author":"L Shao","year":"2008","unstructured":"Shao, L., Ehrgott, M.: Approximating the nondominated set of an MOLP by approximately solving its dual problem. Math. Methods Oper. Res. 68(3), 469\u2013492 (2008)","journal-title":"Math. Methods Oper. Res."}],"container-title":["Journal of Global Optimization"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-013-0136-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10898-013-0136-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-013-0136-0","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T10:59:29Z","timestamp":1565089169000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10898-013-0136-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,1,12]]},"references-count":24,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2014,12]]}},"alternative-id":["136"],"URL":"https:\/\/doi.org\/10.1007\/s10898-013-0136-0","relation":{},"ISSN":["0925-5001","1573-2916"],"issn-type":[{"value":"0925-5001","type":"print"},{"value":"1573-2916","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,1,12]]}}}