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By the Lyapunov analysis approach, we investigate asymptotic properties of the proposed dynamical system as the time $t\\to+\\infty$. The convergence rates are derived for different choices of the damping coefficients. We also show that the obtained results are robust under external perturbations.<\/jats:p>","DOI":"10.1137\/20m1355379","type":"journal-article","created":{"date-parts":[[2021,9,21]],"date-time":"2021-09-21T10:48:51Z","timestamp":1632221331000},"page":"3278-3301","source":"Crossref","is-referenced-by-count":47,"title":["Convergence Rates of Inertial Primal-Dual Dynamical Methods for Separable Convex Optimization Problems"],"prefix":"10.1137","volume":"59","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4896-2482","authenticated-orcid":true,"given":"Xin","family":"He","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Rong","family":"Hu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ya Ping","family":"Fang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2021,9,21]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012998335802"},{"key":"atypb2","first-page":"1","volume":"6","author":"Attouch H.","year":"2021","journal-title":"Minimax Theory Appl."},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2017.06.024"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.3934\/eect.2018018"},{"key":"atypb5","doi-asserted-by":"crossref","unstructured":"H. Attouch, Z. Chbani, J. M. Fadili, and H. Riahi,\n                      Fast convergence of dynamical ADMM via time scaling of damped inertial dynamics\n                      , J. Optim. Theory Appl. (2021),https:\/\/doi.org\/10.1007\/s10957-021-01859-2.","DOI":"10.1007\/s10957-021-01859-2"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-016-0992-8"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1051\/cocv\/2017083"},{"key":"atypb8","unstructured":"H. Attouch, Z. Chbani, and H. Riahi,\n                      Fast convex optimization via time scaling of damped inertial gradient dynamics\n                      , Pure Appl. Funct. Anal., to appear; available athttps:\/\/hal.archives-ouvertes.fr\/hal-02138954\/document, 2020."},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1137\/18M1186757"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.3934\/eect.2017010"},{"key":"atypb11","doi-asserted-by":"crossref","unstructured":"A. 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