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(Comput Optim Appl 58:523\u2013541, 2014. <jats:ext-link xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" ext-link-type=\"doi\" xlink:href=\"https:\/\/doi.org\/10.1007\/s10589-014-9647-y\">10.1007\/s10589-014-9647-y<\/jats:ext-link>) for piecewise linear function fitting. We show that this MINLP model is incomplete and can result in a piecewise linear curve that is not the graph of a function, because it misses a set of necessary constraints. We provide two counterexamples to illustrate this effect, and propose three alternative models that correct this behavior. We investigate the theoretical relationship between these models and evaluate their computational performance.<\/jats:p>","DOI":"10.1007\/s10589-021-00268-5","type":"journal-article","created":{"date-parts":[[2021,3,9]],"date-time":"2021-03-09T12:58:49Z","timestamp":1615294729000},"page":"223-233","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["MINLP formulations for continuous piecewise linear function fitting"],"prefix":"10.1007","volume":"79","author":[{"given":"Noam","family":"Goldberg","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8501-2785","authenticated-orcid":false,"given":"Steffen","family":"Rebennack","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Youngdae","family":"Kim","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Vitaliy","family":"Krasko","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sven","family":"Leyffer","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2021,3,9]]},"reference":[{"key":"268_CR1","doi-asserted-by":"publisher","first-page":"1079","DOI":"10.1080\/01621459.1969.10501038","volume":"64","author":"R Bellman","year":"1969","unstructured":"Bellman, R., Roth, R.: Curve fitting by segmented straight lines. 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