{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,8]],"date-time":"2026-07-08T00:40:10Z","timestamp":1783471210745,"version":"3.55.0"},"reference-count":0,"publisher":"Cambridge University Press (CUP)","license":[{"start":{"date-parts":[[2024,9,4]],"date-time":"2024-09-04T00:00:00Z","timestamp":1725408000000},"content-version":"unspecified","delay-in-days":65,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Acta Numerica"],"published-print":{"date-parts":[[2024,7]]},"abstract":"<jats:p>We propose a geometric framework to describe and analyse a wide array of operator splitting methods for solving monotone inclusion problems. The initial inclusion problem, which typically involves several operators combined through monotonicity-preserving operations, is seldom solvable in its original form. We embed it in an auxiliary space, where it is associated with a surrogate monotone inclusion problem with a more tractable structure and which allows for easy recovery of solutions to the initial problem. The surrogate problem is solved by successive projections onto half-spaces containing its solution set. The outer approximation half-spaces are constructed by using the individual operators present in the model separately. This geometric framework is shown to encompass traditional methods as well as state-of-the-art asynchronous block-iterative algorithms, and its flexible structure provides a pattern to design new ones.<\/jats:p>","DOI":"10.1017\/s0962492923000065","type":"journal-article","created":{"date-parts":[[2024,9,4]],"date-time":"2024-09-04T12:36:28Z","timestamp":1725453388000},"page":"487-632","source":"Crossref","is-referenced-by-count":17,"title":["The geometry of monotone operator splitting methods"],"prefix":"10.1017","volume":"33","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9730-5932","authenticated-orcid":false,"given":"Patrick L.","family":"Combettes","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2024,9,4]]},"container-title":["Acta Numerica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0962492923000065","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,16]],"date-time":"2024-09-16T08:20:05Z","timestamp":1726474805000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0962492923000065\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,7]]},"references-count":0,"alternative-id":["S0962492923000065"],"URL":"https:\/\/doi.org\/10.1017\/s0962492923000065","relation":{},"ISSN":["0962-4929","1474-0508"],"issn-type":[{"value":"0962-4929","type":"print"},{"value":"1474-0508","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,7]]}}}