{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,24]],"date-time":"2026-01-24T14:56:10Z","timestamp":1769266570990,"version":"3.49.0"},"reference-count":26,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2023,5,25]],"date-time":"2023-05-25T00:00:00Z","timestamp":1684972800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Italian Ministry of University"},{"name":"Istituto Nazionale di Alta Matematica-Gruppo Nazionale per il Calcolo Scientifico (INdAM-GNCS)"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>Many data analysis problems can be modeled as a constrained optimization problem characterized by nonsmooth functionals, often because of the presence of \u21131-regularization terms. One of the most effective ways to solve such problems is through the Alternate Direction Method of Multipliers (ADMM), which has been proved to have good theoretical convergence properties even if the arising subproblems are solved inexactly. Nevertheless, experience shows that the choice of the parameter \u03c4 penalizing the constraint violation in the Augmented Lagrangian underlying ADMM affects the method\u2019s performance. To this end, strategies for the adaptive selection of such parameter have been analyzed in the literature and are still of great interest. In this paper, starting from an adaptive spectral strategy recently proposed in the literature, we investigate the use of different strategies based on Barzilai\u2013Borwein-like stepsize rules. We test the effectiveness of the proposed strategies in the solution of real-life consensus logistic regression and portfolio optimization problems.<\/jats:p>","DOI":"10.3390\/a16060264","type":"journal-article","created":{"date-parts":[[2023,5,25]],"date-time":"2023-05-25T02:58:48Z","timestamp":1684983528000},"page":"264","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["On the Adaptive Penalty Parameter Selection in ADMM"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9130-8163","authenticated-orcid":false,"given":"Serena","family":"Crisci","sequence":"first","affiliation":[{"name":"Department of Mathematics and Physics, University of Campania \u201cLuigi Vanvitelli\u201d, Viale Abramo Lincoln, 5, 81100 Caserta, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3357-5252","authenticated-orcid":false,"given":"Valentina","family":"De Simone","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Physics, University of Campania \u201cLuigi Vanvitelli\u201d, Viale Abramo Lincoln, 5, 81100 Caserta, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2140-8094","authenticated-orcid":false,"given":"Marco","family":"Viola","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, University College Dublin, Belfield, D04 V1W8 Dublin, Ireland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,5,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1561\/2200000016","article-title":"Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers","volume":"3","author":"Boyd","year":"2011","journal-title":"Found. 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