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(J Global Optim 64(2):249\u2013272, 2016) rediscovered the supporting hyperplane algorithm of Veinott (Oper Res 15(1):147\u2013152, 1967) and demonstrated its computational benefits for solving convex mixed integer nonlinear programs. In this paper we derive the algorithm from a geometric point of view. This enables us to show that the supporting hyperplane algorithm is equivalent to Kelley\u2019s cutting plane algorithm (J Soc Ind Appl Math 8(4):703\u2013712, 1960) applied to a particular reformulation of the problem. As a result, we extend the applicability of the supporting hyperplane algorithm to convex problems represented by a class of general, not necessarily convex nor differentiable, functions.<\/jats:p>","DOI":"10.1007\/s10898-020-00906-y","type":"journal-article","created":{"date-parts":[[2020,5,13]],"date-time":"2020-05-13T02:03:31Z","timestamp":1589335411000},"page":"161-179","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["On the relation between the extended supporting hyperplane algorithm and Kelley\u2019s cutting plane algorithm"],"prefix":"10.1007","volume":"78","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7892-3951","authenticated-orcid":false,"given":"Felipe","family":"Serrano","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2536-026X","authenticated-orcid":false,"given":"Robert","family":"Schwarz","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0391-5903","authenticated-orcid":false,"given":"Ambros","family":"Gleixner","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,5,13]]},"reference":[{"issue":"4","key":"906_CR1","doi-asserted-by":"publisher","first-page":"703","DOI":"10.1137\/0108053","volume":"8","author":"JE Kelley Jr","year":"1960","unstructured":"Kelley Jr., J.E.: The cutting-plane method for solving convex programs. 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