{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T19:43:49Z","timestamp":1787341429602,"version":"build-2736575974"},"reference-count":15,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Optim."],"published-print":{"date-parts":[[2018,1]]},"abstract":"<jats:p>In a recent paper, Basu, Hildebrand, and Molinaro established that the set of continuous minimal functions for the 1-dimensional Gomory--Johnson infinite group relaxation possesses a dense subset of extreme functions. The $n$-dimensional version of this result was left as an open question. In the present paper, we settle this query in the affirmative: for any integer $n \\geq 1$, every continuous minimal function can be arbitrarily well approximated by an extreme function in the $n$-dimensional Gomory--Johnson model.<\/jats:p>","DOI":"10.1137\/17m1143605","type":"journal-article","created":{"date-parts":[[2018,9,13]],"date-time":"2018-09-13T11:36:05Z","timestamp":1536838565000},"page":"2518-2540","source":"Crossref","is-referenced-by-count":0,"title":["Approximation of Minimal Functions by Extreme Functions"],"prefix":"10.1137","volume":"28","author":[{"given":"Teresa M.","family":"Lebair","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Amitabh","family":"Basu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2018,9,13]]},"reference":[{"key":"atypb1","first-page":"3","author":"Allgower E. L.","year":"1997","journal-title":"Amsterdam"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-015-0890-5"},{"key":"atypb3","first-page":"63","author":"Basu A.","year":"2017","journal-title":"Cham"},{"key":"atypb4","doi-asserted-by":"crossref","unstructured":"A. Basu, R. Hildebrand, and M. Ko\u0308ppe,\n                      Light on the infinite group relaxation I: Foundations and taxonomy\n                      , 4OR, 14 (2016), pp. 1-40,https:\/\/doi.org\/10.1007\/s10288-015-0292-9.","DOI":"10.1007\/s10288-015-0292-9"},{"key":"atypb5","doi-asserted-by":"crossref","unstructured":"A. Basu, R. Hildebrand, and M. Ko\u0308ppe,\n                      Light on the infinite group relaxation II: Sufficient conditions for extremality, sequences, and algorithms\n                      , 4OR, 14 (2016), pp. 1-25,https:\/\/doi.org\/10.1007\/s10288-015-0293-8.","DOI":"10.1007\/s10288-015-0293-8"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1137\/110848608"},{"key":"atypb7","first-page":"202","author":"Basu A.","year":"2016","journal-title":"Cham"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1287\/opre.1110.0916"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1007\/BF01584976"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1007\/BF01585008"},{"key":"atypb11","unstructured":"J. F. Hudson and J. L. Shaneson,\n                      Piecewise Linear Topology\n                      , W. A. Benjamin, New York, Amstersdam, 1969."},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0120692"},{"key":"atypb13","unstructured":"R. T. Rockafellar,\n                      Convex Analysis\n                      , Princeton University Press, Princeton, NJ, 1970."},{"key":"atypb14","doi-asserted-by":"crossref","unstructured":"S. Scholtes,\n                      Introduction to Piecewise Differentiable Equations\n                      , Springer, New York, 2012,https:\/\/doi.org\/10.1007\/978-1-4614-4340-7.","DOI":"10.1007\/978-1-4614-4340-7"},{"key":"atypb15","doi-asserted-by":"crossref","unstructured":"G. M. Ziegler,\n                      Lectures on Polytopes\n                      , Springer, New York, 1995,https:\/\/doi.org\/10.1007\/978-1-4613-8431-1.","DOI":"10.1007\/978-1-4613-8431-1"}],"container-title":["SIAM Journal on Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/17M1143605","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T19:19:30Z","timestamp":1787339970000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/17M1143605"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,1]]},"references-count":15,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2018,1]]}},"alternative-id":["10.1137\/17M1143605"],"URL":"https:\/\/doi.org\/10.1137\/17m1143605","relation":{},"ISSN":["1052-6234","1095-7189"],"issn-type":[{"value":"1052-6234","type":"print"},{"value":"1095-7189","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,1]]}}}