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Using the latter condition and a certain second-order sufficient condition, we are able to establish Q-linear convergence of the primal-dual sequence for an inexact version of the ALM for composite programs.<\/jats:p>\n                  <jats:p>Funding: Research of the first author is partially supported by Singapore National Academy of Science via SASEAF Programme under the grant RIE2025 NRF International Partnership Funding Initiative. Research of the second author is partially supported by the National Science Foundation under the grant DMS 2108546.<\/jats:p>","DOI":"10.1287\/moor.2023.0324","type":"journal-article","created":{"date-parts":[[2025,3,14]],"date-time":"2025-03-14T11:00:52Z","timestamp":1741950052000},"page":"591-620","source":"Crossref","is-referenced-by-count":1,"title":["Convergence of Augmented Lagrangian Methods for Composite Optimization Problems"],"prefix":"10.1287","volume":"51","author":[{"given":"Nguyen Thi","family":"Van Hang","sequence":"first","affiliation":[{"name":"School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 639798; and Institute of Mathematics, Vietnam Academy of Science and Technology, Hanoi 100000, Vietnam"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6049-8902","authenticated-orcid":false,"given":"Ebrahim","family":"Sarabi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Miami University, Oxford, Ohio 45065"}]}],"member":"109","reference":[{"key":"B1","doi-asserted-by":"publisher","DOI":"10.1137\/060654797"},{"issue":"2","key":"B2","first-page":"365","volume":"15","author":"Arag\u00f3n Artacho FJ","year":"2008","journal-title":"J. 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