{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,15]],"date-time":"2026-07-15T13:07:29Z","timestamp":1784120849855,"version":"3.55.0"},"reference-count":27,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","funder":[{"DOI":"10.13039\/501100003977","name":"Israel Science Foundation","doi-asserted-by":"publisher","award":["2480-21"],"award-info":[{"award-number":["2480-21"]}],"id":[{"id":"10.13039\/501100003977","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003977","name":"Israel Science Foundation","doi-asserted-by":"publisher","award":["2619-20"],"award-info":[{"award-number":["2619-20"]}],"id":[{"id":"10.13039\/501100003977","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Optim."],"published-print":{"date-parts":[[2026,9,30]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>In this paper, we study convex bilevel optimization problems where both the inner and outer levels are given as a composite convex minimization. We propose the Fast Bilevel Proximal Gradient (FBi-PG) algorithm, which can be interpreted as applying FISTA to a dynamic regularized composite objective function. The dynamic nature of the regularization parameters allows one to achieve an optimal fast convergence rate of [Formula: see text] in terms of the inner objective function. This is the fastest known convergence rate under no additional restrictive assumptions. We also show that FBi-PG achieves sublinear simultaneous rates in terms of both the inner and outer objective functions. Moreover, we show that under a H\u00f6lderian type error bound assumption on the inner objective function, the FBi-PG algorithm achieves improved simultaneous rates and converges to an optimal solution of the bilevel optimization problem. Finally, we present numerical experiments demonstrating the performance of the proposed scheme.<\/jats:p>","DOI":"10.1137\/25m1767893","type":"journal-article","created":{"date-parts":[[2026,7,15]],"date-time":"2026-07-15T12:38:38Z","timestamp":1784119118000},"page":"1476-1508","source":"Crossref","is-referenced-by-count":0,"title":["Dynamic FISTA for Convex Composite Bilevel Optimization"],"prefix":"10.1137","volume":"36","author":[{"given":"Roey","family":"Merchav","sequence":"first","affiliation":[{"name":"Faculty of Industrial Engineering and Management, Technion\u2013Israel Institute of Technology, Haifa 3200003, Israel."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shoham","family":"Sabach","sequence":"additional","affiliation":[{"name":"Faculty of Industrial Engineering and Management, Technion\u2013Israel Institute of Technology, Haifa 3200003, Israel."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4228-131X","authenticated-orcid":true,"given":"Marc","family":"Teboulle","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Tel-Aviv University, Ramat-Aviv 69978, Israel."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2026,7,15]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2009.06.014"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623403427823"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4419-9467-7"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1137\/080716542"},{"key":"ref5","first-page":"42","volume-title":"Convex Optimization in Signal Processing and Communications","author":"Beck A.","year":"2010"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-016-1091-6"},{"key":"ref7","doi-asserted-by":"crossref","unstructured":"R. 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