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Further characterizations of these notions are derived by using generalized differentiation of variational analysis in the framework of Hilbert spaces.<\/jats:p>\n                  <jats:p>Funding: This research was supported by the U.S. National Science Foundation [Grants DMS-1808978 and DMS-2204519], the Australian Research Council Discovery Project [Grant DP-190100555], and Project 111 of China [Grant D21024].<\/jats:p>","DOI":"10.1287\/moor.2023.0270","type":"journal-article","created":{"date-parts":[[2025,4,25]],"date-time":"2025-04-25T11:01:24Z","timestamp":1745578884000},"page":"938-955","source":"Crossref","is-referenced-by-count":2,"title":["Local Maximal Monotonicity in Variational Analysis and Optimization"],"prefix":"10.1287","volume":"51","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7156-1380","authenticated-orcid":false,"given":"Pham Duy","family":"Khanh","sequence":"first","affiliation":[{"name":"Group of Analysis and Applied Mathematics, Department of Mathematics, Ho Chi Minh City University of Education, Ho Chi Minh City 700000, Vietnam"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0001-9213-1061","authenticated-orcid":false,"given":"Vu Vinh Huy","family":"Khoa","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Wayne State University, Detroit, Michigan 48202"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6071-6049","authenticated-orcid":false,"given":"Boris S.","family":"Mordukhovich","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Wayne State University, Detroit, Michigan 48202"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1211-8025","authenticated-orcid":false,"given":"Vo Thanh","family":"Phat","sequence":"additional","affiliation":[{"name":"Department of Mathematics & Statistics, University of North Dakota, Grand Forks, North Dakota 58202"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"109","reference":[{"key":"B1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-48311-5"},{"issue":"2","key":"B2","first-page":"461","volume":"23","author":"Chieu NH","year":"2016","journal-title":"J. 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