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Optim."],"published-print":{"date-parts":[[2025,9,30]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>In this work, we are concerned with the decentralized optimization problem: [Formula: see text] where [Formula: see text] is a convex domain and each [Formula: see text] is a local cost function only known to agent [Formula: see text]. A fundamental algorithm for this problem is the decentralized projected gradient method (DPG) given by [Formula: see text] where [Formula: see text] is the projection operator to [Formula: see text] and [Formula: see text] are communication weight among the agents. While this method has been widely used in the literature, its convergence property has not been established so far, except for the special case [Formula: see text]. This work establishes new convergence estimates of DPG when the aggregate cost [Formula: see text] is strongly convex and each function [Formula: see text] is smooth. If the stepsize [Formula: see text] is suitably small, we prove that each [Formula: see text] converges linearly to an [Formula: see text]-neighborhood of the minimizer. In addition, we further improve the convergence result by showing that the point [Formula: see text] converges linearly to an [Formula: see text]-neighborhood of the minimizer if the domain is given by the half-space [Formula: see text] for any dimension [Formula: see text]. Numerical experiments are provided to support the convergence results.<\/jats:p>","DOI":"10.1137\/23m1562032","type":"journal-article","created":{"date-parts":[[2025,8,6]],"date-time":"2025-08-06T08:00:20Z","timestamp":1754467220000},"page":"1673-1702","source":"Crossref","is-referenced-by-count":2,"title":["On the Convergence Analysis of the Decentralized Projected Gradient Descent Method"],"prefix":"10.1137","volume":"35","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0238-1655","authenticated-orcid":true,"given":"Woocheol","family":"Choi","sequence":"first","affiliation":[{"name":"Department of Mathematics, Sungkyunkwan University, 2066 Seobu-ro, Jangan-gu, Suwon-si, Gyeonggi-do, 16419 Republic of Korea."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jimyeong","family":"Kim","sequence":"additional","affiliation":[{"name":"R&D Center, Samsung SDS, Seoul, 05510 Republic of Korea."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2025,8,6]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1109\/TCNS.2015.2505149"},{"key":"ref2","unstructured":"M. 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