{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,17]],"date-time":"2026-04-17T03:40:40Z","timestamp":1776397240984,"version":"3.51.2"},"reference-count":15,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2025,11,30]],"date-time":"2025-11-30T00:00:00Z","timestamp":1764460800000},"content-version":"vor","delay-in-days":333,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2025,1]]},"abstract":"<jats:p>\n                    This paper presents a comprehensive stability analysis of regularized Newton methods for solving monotone inclusion problems of the form 0 \u2208\n                    <jats:italic>A<\/jats:italic>\n                    (\n                    <jats:italic>x<\/jats:italic>\n                    ) +\n                    <jats:italic>F<\/jats:italic>\n                    (\n                    <jats:italic>x<\/jats:italic>\n                    ), where\n                    <jats:italic>A<\/jats:italic>\n                    is a maximal monotone operator and\n                    <jats:italic>F<\/jats:italic>\n                    is a Lipschitz continuous operator with bounded variation. By modeling the problem as a dynamical system, we analyze its stability using a Lyapunov function approach, establishing existence, uniqueness, and exponential convergence under strong monotonicity conditions. The bounded variation property enables tighter convergence bounds compared to traditional methods. Numerical experiments validate the theoretical results, demonstrating robust stability in nonsmooth optimization contexts. The findings extend to applications in machine learning, distributed optimization, and dynamic networks, offering insights into adaptive regularization strategies and practical implementations.\n                  <\/jats:p>","DOI":"10.1155\/jama\/6663632","type":"journal-article","created":{"date-parts":[[2025,12,1]],"date-time":"2025-12-01T05:48:32Z","timestamp":1764568112000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Advanced Stability Analysis of Regularized Newton Methods for Monotone Inclusions With Bounded Variation"],"prefix":"10.1155","volume":"2025","author":[{"ORCID":"https:\/\/orcid.org\/0009-0001-0161-3699","authenticated-orcid":false,"given":"Boushra","family":"Abbas","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2025,11,30]]},"reference":[{"key":"e_1_2_13_1_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-48311-5"},{"key":"e_1_2_13_2_2","first-page":"30","article-title":"Stability of a Regularized Newton Method With Two Potentials","volume":"1","author":"Abbas B.","year":"2020","journal-title":"International Journal of Theoretical and Applied Mathematics"},{"key":"e_1_2_13_3_2","first-page":"6020","article-title":"Fully Distributed Nash Equilibrium Seeking Over Time-Varying Communication Networks With Linear Convergence Rate","volume":"66","author":"Bianchi M.","year":"2021","journal-title":"IEEE Transactions on Automatic Control"},{"key":"e_1_2_13_4_2","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1970-0282272-5"},{"key":"e_1_2_13_5_2","first-page":"1","article-title":"New Newton-Type Methods for Unconstrained Optimization","volume":"30","author":"Polyak B. 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K.","year":"2002"},{"key":"e_1_2_13_13_2","volume-title":"Convex Analysis and Monotone Operator Theory. CMS Books in Mathematics","author":"Bauschke H.","year":"2011"},{"key":"e_1_2_13_14_2","unstructured":"AgarwalN. BullinsB. ChenX. HazanE. SinghK. ZhangC. andZhangY. Efficient Full-Matrix Adaptive Regularization International Conference on Machine Learning (ICML) 2021 PMLR."},{"key":"e_1_2_13_15_2","first-page":"1","article-title":"Large-Scale Convex Optimization: Algorithms and Analysis","volume":"4","author":"Ryu E. K.","year":"2020","journal-title":"Foundations and Trends in Optimization"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/jama\/6663632","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1155\/jama\/6663632","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/jama\/6663632","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,17]],"date-time":"2026-04-17T02:41:39Z","timestamp":1776393699000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/jama\/6663632"}},"subtitle":[],"editor":[{"given":"Anwarud","family":"Din","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2025,1]]},"references-count":15,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2025,1]]}},"alternative-id":["10.1155\/jama\/6663632"],"URL":"https:\/\/doi.org\/10.1155\/jama\/6663632","archive":["Portico"],"relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"value":"1110-757X","type":"print"},{"value":"1687-0042","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,1]]},"assertion":[{"value":"2025-08-06","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-10-06","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-11-30","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"6663632"}}