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(J Optim Theory Appl 183(2):490\u2013519, 2019) recently showed that the Douglas\u2013Rachford algorithm provides certificates of infeasibility for a class of convex optimization problems. In particular, they showed that the difference between consecutive iterates generated by the algorithm converges to certificates of primal and dual strong infeasibility. Their result was shown in a finite-dimensional Euclidean setting and for a particular structure of the constraint set. In this paper, we extend the result to real Hilbert spaces and a general nonempty closed convex set. Moreover, we show that the proximal-point algorithm applied to the set of optimality conditions of the problem generates similar infeasibility certificates.<\/jats:p>","DOI":"10.1007\/s11590-021-01706-3","type":"journal-article","created":{"date-parts":[[2021,2,4]],"date-time":"2021-02-04T17:38:43Z","timestamp":1612460323000},"page":"2719-2732","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["On the asymptotic behavior of the Douglas\u2013Rachford and proximal-point algorithms for convex optimization"],"prefix":"10.1007","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6038-1587","authenticated-orcid":false,"given":"Goran","family":"Banjac","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"John","family":"Lygeros","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,2,4]]},"reference":[{"key":"1706_CR1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-48311-5","volume-title":"Convex Analysis and Monotone Operator Theory in Hilbert Spaces","author":"HH Bauschke","year":"2017","unstructured":"Bauschke, H.H., Combettes, P.L.: Convex Analysis and Monotone Operator Theory in Hilbert Spaces, 2nd edn. 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