{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T19:23:47Z","timestamp":1787340227475,"version":"build-2736575974"},"reference-count":38,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","funder":[{"DOI":"10.13039\/501100006595","name":"UEFISCDI","doi-asserted-by":"crossref","award":["PN-III-P4-PCE-2021-0720"],"award-info":[{"award-number":["PN-III-P4-PCE-2021-0720"]}],"id":[{"id":"10.13039\/501100006595","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/100010665","name":"H2020 Marie Sk\u0142odowska-Curie Actions","doi-asserted-by":"publisher","award":["861137"],"award-info":[{"award-number":["861137"]}],"id":[{"id":"10.13039\/100010665","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Optim."],"published-print":{"date-parts":[[2026,3,31]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>In this paper, we introduce a higher-order method for solving composite (non)convex minimization problems with constraints expressed as inequalities involving smooth (non)convex functions. Starting from a feasible point, at each iteration, our method approximates the smooth part of the objective function and of the constraints by higher-order Taylor approximations, leading to a moving Taylor approximation (MTA) method. We present convergence guarantees for the MTA algorithm for both nonconvex and convex problems. In particular, when the objective and the constraints are nonconvex functions, and assuming some regularity condition on the constraints at any point in some sublevel set, we prove that the sequence generated by the MTA algorithm converges globally to a KKT point. Moreover, we derive convergence rates in the iterates when the problem\u2019s data satisfy the Kurdyka\u2013\u0141ojasiewicz property. Further, when the objective function is (uniformly) convex and the constraints are also convex, we provide (linear\/superlinear) sublinear convergence rates for our algorithm. Finally, we present an efficient implementation of the proposed algorithm and compare it with some existing methods from the literature.<\/jats:p>","DOI":"10.1137\/23m1576852","type":"journal-article","created":{"date-parts":[[2026,2,25]],"date-time":"2026-02-25T08:17:16Z","timestamp":1772007436000},"page":"290-319","source":"Crossref","is-referenced-by-count":0,"title":["Moving Higher-Order Taylor Approximations Method for Smooth Constrained Minimization Problems"],"prefix":"10.1137","volume":"36","author":[{"ORCID":"https:\/\/orcid.org\/0009-0004-9805-8039","authenticated-orcid":true,"given":"Yassine","family":"Nabou","sequence":"first","affiliation":[{"name":"Automatic Control and Systems Engineering Department, National University of Science and Technology Politehnica Bucharest 060042, Romania."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ion","family":"Necoara","sequence":"additional","affiliation":[{"name":"Automatic Control and Systems Engineering Department, National University of Science and Technology Politehnica Bucharest and Gheorghe Mihoc-Caius Iacob Institute of Mathematical Statistics and Applied Mathematics of Romanian Academy, Bucharest 060042, Romania."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2026,2,25]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1080\/10556788.2013.841692"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1137\/090777189"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1137\/090763317"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1007\/BF00933176"},{"key":"ref5","volume-title":"Constrained Optimization and Lagrange Multiplier Methods","author":"Bertsekas D.","year":"1982"},{"key":"ref6","volume-title":"Nonlinear Programming","author":"Bertsekas D.","year":"1999","edition":"2"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1137\/15M1031631"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1017\/S0962492900002518"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1137\/060670080"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-019-01382-3"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1287\/moor.2015.0735"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1287\/moor.2017.0900"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1137\/16M1106316"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1080\/10556788.2019.1678033"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611976991"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1109\/TWC.2007.05960"},{"key":"ref17","unstructured":"N. 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