{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,3]],"date-time":"2026-04-03T19:36:07Z","timestamp":1775244967812,"version":"3.50.1"},"reference-count":0,"publisher":"European Mathematical Society - EMS - Publishing House GmbH","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Port. Math."],"published-print":{"date-parts":[[2019,6,6]]},"abstract":"<jats:p>In this note, we develop Fourier approximation methods for the solutions of first-order nonlocal mean-field games (MFG) systems. Using Fourier expansion techniques, we approximate a given MFG system by a simpler one that is equivalent to a convex optimization problem over a finite-dimensional subspace of continuous curves. Furthermore, we perform a time-discretization for this optimization problem and arrive at a finite-dimensional saddle point problem. Finally, we solve this saddle-point problem by a variant of a primal dual hybrid gradient method.<\/jats:p>","DOI":"10.4171\/pm\/2023","type":"journal-article","created":{"date-parts":[[2019,6,6]],"date-time":"2019-06-06T17:30:16Z","timestamp":1559842216000},"page":"367-396","source":"Crossref","is-referenced-by-count":19,"title":["Fourier approximation methods for first-order nonlocal mean-field games"],"prefix":"10.4171","volume":"75","author":[{"given":"Levon","family":"Nurbekyan","sequence":"first","affiliation":[{"name":"McGill University, Montreal, Canada"}]},{"given":"Jo\u00e3o","family":"Sa\u00fade","sequence":"additional","affiliation":[{"name":"Carnegie Mellon University, Pittsburgh, USA"}]}],"member":"2673","container-title":["Portugaliae Mathematica"],"original-title":[],"link":[{"URL":"https:\/\/www.ems-ph.org\/fulltext\/10.4171\/PM\/2023","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,4]],"date-time":"2025-11-04T13:12:49Z","timestamp":1762261969000},"score":1,"resource":{"primary":{"URL":"https:\/\/ems.press\/doi\/10.4171\/pm\/2023"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,6,6]]},"references-count":0,"journal-issue":{"issue":"3"},"URL":"https:\/\/doi.org\/10.4171\/pm\/2023","relation":{},"ISSN":["0032-5155","1662-2758"],"issn-type":[{"value":"0032-5155","type":"print"},{"value":"1662-2758","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,6,6]]}}}