{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T20:26:30Z","timestamp":1775507190388,"version":"3.50.1"},"reference-count":14,"publisher":"Springer Science and Business Media LLC","issue":"8","license":[{"start":{"date-parts":[[2022,3,13]],"date-time":"2022-03-13T00:00:00Z","timestamp":1647129600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,3,13]],"date-time":"2022-03-13T00:00:00Z","timestamp":1647129600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/100014440","name":"ministerio de ciencia, innovaci\u00f3n y universidades","doi-asserted-by":"publisher","award":["PGC2018-097960-B-C22"],"award-info":[{"award-number":["PGC2018-097960-B-C22"]}],"id":[{"id":"10.13039\/100014440","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Optim Lett"],"published-print":{"date-parts":[[2022,11]]},"DOI":"10.1007\/s11590-022-01865-x","type":"journal-article","created":{"date-parts":[[2022,3,13]],"date-time":"2022-03-13T13:02:32Z","timestamp":1647176552000},"page":"2501-2510","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Duality for convex infinite optimization on linear spaces"],"prefix":"10.1007","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5363-7991","authenticated-orcid":false,"given":"M. A.","family":"Goberna","sequence":"first","affiliation":[]},{"given":"M.","family":"Volle","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,3,13]]},"reference":[{"key":"1865_CR1","doi-asserted-by":"publisher","first-page":"163","DOI":"10.1007\/BF00934766","volume":"37","author":"CE Blair","year":"1982","unstructured":"Blair, C.E., Duffin, R.J., Jeroslow, R.G.: A limiting infisup theorem. J. Optim. Theory Appl. 37, 163\u2013175 (1982)","journal-title":"J. Optim. Theory Appl."},{"key":"1865_CR2","doi-asserted-by":"publisher","first-page":"330","DOI":"10.1007\/BF01588327","volume":"18","author":"JM Borwein","year":"1980","unstructured":"Borwein, J.M.: A note on perfect duality and limiting Lagrangeans. Math. Programm. 18, 330\u2013337 (1980)","journal-title":"Math. Programm."},{"key":"1865_CR3","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-04900-2","volume-title":"Conjugate Duality in Convex Optimization","author":"RI Bo\u0163","year":"2010","unstructured":"Bo\u0163, R.I.: Conjugate Duality in Convex Optimization. Springer, Berlin\/Heidelberg (2010)"},{"key":"1865_CR4","doi-asserted-by":"crossref","unstructured":"Dinh, N., Goberna, M.A., L\u00f3pez, M.A., Volle, M.: Relaxed Lagrangian duality in convex infinite optimization: reverse strong duality and optimality. J. Appl. Numer. Optim. 4, 3\u201318 (2022)","DOI":"10.23952\/jano.4.2022.1.02"},{"key":"1865_CR5","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1007\/BF01584656","volume":"4","author":"RJ Duffin","year":"1973","unstructured":"Duffin, R.J.: Convex analysis treated by linear programming. Math. Programm. 4, 125\u2013143 (1973)","journal-title":"Math. Programm."},{"key":"1865_CR6","unstructured":"Duffin, R.J., Jeroslow, R.G.: The Limiting Lagrangian. Georgia Institute of Technology, Management Science Technical Reports No. MS-79-13 (1979)"},{"key":"1865_CR7","volume-title":"Linear Semi-Infinite Optimization","author":"MA Goberna","year":"1998","unstructured":"Goberna, M.A., L\u00f3pez, M.A.: Linear Semi-Infinite Optimization. Wiley, Chichester, U.K. (1998)"},{"key":"1865_CR8","doi-asserted-by":"publisher","first-page":"75","DOI":"10.1007\/BF02591965","volume":"27","author":"DF Karney","year":"1983","unstructured":"Karney, D.F.: A duality theorem for semi-infinite convex programs and their finite subprograms. Math. Programm. 27, 75\u201382 (1983)","journal-title":"Math. Programm."},{"key":"1865_CR9","doi-asserted-by":"publisher","first-page":"163","DOI":"10.1007\/BF00938595","volume":"48","author":"DF Karney","year":"1986","unstructured":"Karney, D.F., Morley, T.D.: Limiting Lagrangians: a primal approach. J Optim. Theory Appl. 48, 163\u2013174 (1986)","journal-title":"J Optim. Theory Appl."},{"key":"1865_CR10","doi-asserted-by":"crossref","unstructured":"Lemaire, B., Volle, M.: Duality in DC programming. Generalized convexity, generalized monotonicity: recent results (Luminy, 1996), 331-345, Nonconvex Optim. Appl. 27, Kluwer, Dordrecht (1998)","DOI":"10.1007\/978-1-4613-3341-8_15"},{"key":"1865_CR11","doi-asserted-by":"publisher","first-page":"661","DOI":"10.1007\/s11228-021-00596-y","volume":"29","author":"DT Luc","year":"2021","unstructured":"Luc, D.T., Volle, M.: Algebraic approach to duality in optimization and applications. Set-Valued Var. Anal. 29, 661\u2013681 (2021)","journal-title":"Set-Valued Var. Anal."},{"key":"1865_CR12","doi-asserted-by":"publisher","first-page":"238","DOI":"10.1007\/BF02591888","volume":"30","author":"J-Ch Pomerol","year":"1984","unstructured":"Pomerol, J.-Ch.: A note on limiting infisup theorems. Math. Program. 30, 238\u2013241 (1984)","journal-title":"Math. Program."},{"key":"1865_CR13","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611970524","volume-title":"Conjugate Duality and Optimization","author":"RT Rockafellar","year":"1974","unstructured":"Rockafellar, R.T.: Conjugate Duality and Optimization. SIAM, Philadelphia, P.A. (1974)"},{"key":"1865_CR14","doi-asserted-by":"publisher","DOI":"10.1142\/5021","volume-title":"Convex Analysis in General Vector Spaces.","author":"C Z\u0103linescu","year":"2002","unstructured":"Z\u0103linescu, C.: Convex Analysis in General Vector Spaces. World Scientific, River Edge, N.J. (2002)"}],"updated-by":[{"DOI":"10.1007\/s11590-022-01876-8","type":"correction","label":"Correction","source":"publisher","updated":{"date-parts":[[2022,3,30]],"date-time":"2022-03-30T00:00:00Z","timestamp":1648598400000}}],"container-title":["Optimization Letters"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11590-022-01865-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11590-022-01865-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11590-022-01865-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,10,6]],"date-time":"2022-10-06T12:57:46Z","timestamp":1665061066000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11590-022-01865-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,3,13]]},"references-count":14,"journal-issue":{"issue":"8","published-print":{"date-parts":[[2022,11]]}},"alternative-id":["1865"],"URL":"https:\/\/doi.org\/10.1007\/s11590-022-01865-x","relation":{"correction":[{"id-type":"doi","id":"10.1007\/s11590-022-01876-8","asserted-by":"object"}]},"ISSN":["1862-4472","1862-4480"],"issn-type":[{"value":"1862-4472","type":"print"},{"value":"1862-4480","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,3,13]]},"assertion":[{"value":"20 June 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 February 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 March 2022","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"30 March 2022","order":4,"name":"change_date","label":"Change Date","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"Correction","order":5,"name":"change_type","label":"Change Type","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"A Correction to this paper has been published:","order":6,"name":"change_details","label":"Change Details","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"https:\/\/doi.org\/10.1007\/s11590-022-01876-8","URL":"https:\/\/doi.org\/10.1007\/s11590-022-01876-8","order":7,"name":"change_details","label":"Change Details","group":{"name":"ArticleHistory","label":"Article History"}}]}}