{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,29]],"date-time":"2026-08-29T05:18:01Z","timestamp":1787980681912,"version":"build-2784847793"},"reference-count":18,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2026,8,27]],"date-time":"2026-08-27T00:00:00Z","timestamp":1787788800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100009076","name":"University of Science and Technology of China","doi-asserted-by":"crossref","award":["KY2040002501"],"award-info":[{"award-number":["KY2040002501"]}],"id":[{"id":"10.13039\/501100009076","id-type":"DOI","asserted-by":"crossref"}]},{"award":["KY2040002501"],"award-info":[{"award-number":["KY2040002501"]}],"id":[{"id":"https:\/\/ror.org\/04c4dkn09","id-type":"ROR","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000038","name":"Natural Science and Engineering Research Council of Canada","doi-asserted-by":"crossref","award":["RGPIN-2023-05655"],"award-info":[{"award-number":["RGPIN-2023-05655"]}],"id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this paper, we study the generalized nearly isotonic optimization (GNIO) model and its dynamic programming solution (GNIO-DP). We introduce randomness into the GNIO-DP algorithm, enabling its first application to change-point detection and resulting in an O(n) complexity multiple change-point detection method. At the same time, we provide the theoretical properties of the change-point detection and prove the reliability and effectiveness of the GNIO-DP algorithm for this task. The simulation results show that our method has strong change-point detection ability. Compared with traditional methods, our method is faster in most scenarios.<\/jats:p>","DOI":"10.3390\/e28090961","type":"journal-article","created":{"date-parts":[[2026,8,27]],"date-time":"2026-08-27T13:26:03Z","timestamp":1787837163000},"page":"961","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Fast Multiple Change-Point Detection Method via Generalized Nearly Isotonic Optimization"],"prefix":"10.3390","volume":"28","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3244-6317","authenticated-orcid":false,"given":"Luoxin","family":"Wang","sequence":"first","affiliation":[{"name":"Department of Statistics and Finance, University of Science and Technology of China, Hefei 230026, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mengmeng","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Mathematics and System Science, Xinjiang University, Urumqi 830017, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Baisuo","family":"Jin","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Xinjiang Normal University, Urumqi 830017, China"},{"name":"Department of Statistics and Finance, University of Science and Technology of China, Hefei 230026, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8858-1289","authenticated-orcid":false,"given":"Yuehua","family":"Wu","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, York University, Toronto, ON M3J 1P3, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,8,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"123630","DOI":"10.1016\/j.physa.2019.123630","article-title":"Change point analysis on the Corinth Gulf (Greece) seismicity","volume":"541","author":"Lykou","year":"2020","journal-title":"Phys. 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