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Optim."],"published-print":{"date-parts":[[2026,9,30]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>In this work, we develop a convergence framework for iterative algorithms whose updates can be described by a one-parameter family of nonexpansive operators. Within the framework, each step involving one of the main algorithmic operators is followed by a second step which \u201crelocates\u201d fixed points of the current operator to the next. As a consequence, our analysis does not require the family of nonexpansive operators to have a common fixed point, as frequently assumed in the literature. Our analysis uses a parametric extension of the demiclosedness principle for nonexpansive operators.\u00a0As an application of our convergence results, we develop a version of the graph-based extension of the Douglas\u2013Rachford algorithm for finding a zero of the sum of [Formula: see text] maximally monotone operators, which does not require the resolvent parameter to be constant across iterations.<\/jats:p>","DOI":"10.1137\/25m1776810","type":"journal-article","created":{"date-parts":[[2026,7,8]],"date-time":"2026-07-08T18:36:28Z","timestamp":1783535788000},"page":"1297-1325","source":"Crossref","is-referenced-by-count":0,"title":["Relocated Fixed-Point Iterations with Applications to Variable Stepsize Resolvent Splitting"],"prefix":"10.1137","volume":"36","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8577-697X","authenticated-orcid":true,"given":"Felipe","family":"Atenas","sequence":"first","affiliation":[{"name":"Centro de Modelamiento Matem\u00e1tico (CNRS IRL2807), Santiago, Chile."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4155-9930","authenticated-orcid":true,"given":"Heinz H.","family":"Bauschke","sequence":"additional","affiliation":[{"name":"Mathematics, University of British Columbia, Kelowna, B.C. 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