{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,20]],"date-time":"2025-05-20T04:01:29Z","timestamp":1747713689817,"version":"3.40.5"},"reference-count":34,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2024,4,25]],"date-time":"2024-04-25T00:00:00Z","timestamp":1714003200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2024,4,25]],"date-time":"2024-04-25T00:00:00Z","timestamp":1714003200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"Universit\u00e0 degli Studi di Roma La Sapienza"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Dyn Games Appl"],"published-print":{"date-parts":[[2025,5]]},"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:p>We analyze asymptotic convergence properties of Newton\u2019s method for a class of evolutive Mean Field Games systems with non-separable Hamiltonian arising in mean field type models with congestion. We prove the well posedness of the Mean Field Game system with non-separable Hamiltonian and of the linear system giving the Newton iterations. Then, by forward induction and assuming that the initial guess is sufficiently close to the solution of problem, we show a quadratic rate of convergence for the approximation of the Mean Field Game system by Newton\u2019s method. We also consider the case of a nonlocal coupling, but with separable Hamiltonian, and we show a similar rate of convergence.\n<\/jats:p>","DOI":"10.1007\/s13235-024-00561-y","type":"journal-article","created":{"date-parts":[[2024,4,25]],"date-time":"2024-04-25T08:02:36Z","timestamp":1714032156000},"page":"534-557","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["On the Quadratic Convergence of Newton\u2019s Method for Mean Field Games with Non-separable Hamiltonian"],"prefix":"10.1007","volume":"15","author":[{"given":"Fabio","family":"Camilli","sequence":"first","affiliation":[]},{"given":"Qing","family":"Tang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,4,25]]},"reference":[{"issue":"3","key":"561_CR1","doi-asserted-by":"publisher","first-page":"1136","DOI":"10.1137\/090758477","volume":"48","author":"Y Achdou","year":"2010","unstructured":"Achdou Y, Capuzzo Dolcetta I (2010) Mean field games: numerical methods. 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