{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,23]],"date-time":"2026-10-23T20:34:12Z","timestamp":1792787652862,"version":"4.5.0"},"reference-count":52,"publisher":"SAGE Publications","issue":"4","license":[{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"funder":[{"name":"CEA Youth Key Project on Earthquake Information","award":["CEAITNS202607"],"award-info":[{"award-number":["CEAITNS202607"]}]},{"name":"Earthquake Science Technology Innovation Team Project of Yunnan Province","award":["CXTD202507"],"award-info":[{"award-number":["CXTD202507"]}]},{"name":"Spark Program of Earthquake Sciences of China Earthquake Administration","award":["XH25033YB"],"award-info":[{"award-number":["XH25033YB"]}],"id":[{"id":"https:\/\/ror.org\/045sza929","id-type":"ROR","asserted-by":"crossref"}]}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Science Progress"],"published-print":{"date-parts":[[2026,10]]},"abstract":"<jats:p>\n                    In this paper, we consider a class of multiblock nonconvex nonsmooth optimization problems, which covers many applications such as the analysis of pre-earthquake anomalies and machine learning. To solve this class of problems, we propose the inertial block proximal linearized method with two-phase adaptive momentum (IBPL\n                    <jats:sup>+<\/jats:sup>\n                    -TP). Compared to the current methods, our method possesses three main advantages: (1) it introduces a two-phase adaptive momentum strategy to effectively update the extrapolation parameters, (2) it allows using two different extrapolation points to accelerate the convergence, (3) it allows the extrapolation parameters of these two extrapolation points to be independent of and unconstrained by all other parameters. While maintaining the above advantages, we prove that our method ensures the monotonic convergence of the objective function of this class of problems, and we also prove that the sequence generated by our method globally converges to a critical point, as well as establish the convergence rate of our method. To demonstrate the effectiveness of our method, we apply it to solve two nonconvex and nonsmooth machine learning problems, namely sparse nonnegative matrix factorization with\n                    <jats:italic toggle=\"yes\">\u2113<\/jats:italic>\n                    <jats:sub>0<\/jats:sub>\n                    -constraints and sparse nonnegative CP decomposition with\n                    <jats:italic toggle=\"yes\">\u2113<\/jats:italic>\n                    <jats:sub>0<\/jats:sub>\n                    -constraints. The numerical experimental results on solving these problems show that our method outperforms several state-of-the-art methods.\n                  <\/jats:p>","DOI":"10.1177\/00368504261455343","type":"journal-article","created":{"date-parts":[[2026,10,12]],"date-time":"2026-10-12T09:32:30Z","timestamp":1791797550000},"update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["An inertial block proximal linearized method with adaptive momentum for nonconvex and nonsmooth optimization"],"prefix":"10.1177","volume":"109","author":[{"ORCID":"https:\/\/orcid.org\/0009-0004-9453-3525","authenticated-orcid":false,"given":"Weifeng","family":"Yang","sequence":"first","affiliation":[{"name":"Yunnan Earthquake Agency"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"179","published-online":{"date-parts":[[2026,10,12]]},"reference":[{"key":"e_1_3_4_2_2","doi-asserted-by":"publisher","DOI":"10.3389\/feart.2021.621976"},{"issue":"1","key":"e_1_3_4_3_2","first-page":"100189","article-title":"DTPP:An efficient depthwise separable TCN for seismic phase picking","volume":"7","author":"Lv S","year":"2026","unstructured":"Lv S, Peng Y. 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