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In particular, we study the non-asymptotic properties of the Euler\u2013Maruyama discretization of the Langevin equation, where the forward\u2013backward envelope is used to deal with the non-smooth part of the dynamics. An advantage of this envelope, when compared to widely-used Moreu\u2013Yoshida one and the MYULA algorithm, is that it maintains the MAP estimator of the original non-smooth distribution. We also study a number of numerical experiments that support our theoretical findings.<\/jats:p>","DOI":"10.1007\/s11222-023-10254-y","type":"journal-article","created":{"date-parts":[[2023,5,31]],"date-time":"2023-05-31T18:06:29Z","timestamp":1685556389000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["The forward\u2013backward envelope for sampling with the overdamped Langevin algorithm"],"prefix":"10.1007","volume":"33","author":[{"given":"Armin","family":"Eftekhari","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Luis","family":"Vargas","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3860-9167","authenticated-orcid":false,"given":"Konstantinos C.","family":"Zygalakis","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,5,31]]},"reference":[{"issue":"4","key":"10254_CR1","doi-asserted-by":"publisher","first-page":"1600","DOI":"10.1137\/130935616","volume":"52","author":"A Abdulle","year":"2014","unstructured":"Abdulle, A., Vilmart, G., Zygalakis, K.C.: High order numerical approximation of the invariant measure of ergodic SDEs. 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