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This surprising result goes in line with recent developments on slope determination (Boulmezaoud et al. in SIAM J Optim 28(3):2049\u20132066, 2018; P\u00e9rez-Aros et al. in Math Program 190(1\u20132):561-583, 2021) and slope sensitivity (Daniilidis and Drusvyatskiy in Proc Am Math Soc 151(11):4751-4756, 2023) for convex functions.<\/jats:p>","DOI":"10.1007\/s10107-024-02108-w","type":"journal-article","created":{"date-parts":[[2024,6,20]],"date-time":"2024-06-20T13:02:12Z","timestamp":1718888532000},"page":"319-348","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A slope generalization of Attouch theorem"],"prefix":"10.1007","volume":"212","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4837-694X","authenticated-orcid":false,"given":"Aris","family":"Daniilidis","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"David","family":"Salas","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sebasti\u00e1n","family":"Tapia-Garc\u00eda","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,6,20]]},"reference":[{"key":"2108_CR1","unstructured":"Ambrosio, L., Gigli, N., Savar\u00e9, G.: Gradient Flows in Metric Spaces and in the Space of Probability Measures, 2nd edn. 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