{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T19:41:09Z","timestamp":1787341269564,"version":"build-2736575974"},"reference-count":34,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Optim."],"published-print":{"date-parts":[[2026,6,30]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>In this manuscript, we address continuous unconstrained multiobjective optimization problems and we discuss descent type methods for the reconstruction of the Pareto set. Specifically, we analyze the class of Front Descent methods, which generalizes the Front Steepest Descent algorithm allowing the employment of suitable, effective search directions (e.g., Newton, Quasi-Newton, Barzilai-Borwein). We provide a deep characterization of the behavior and the mechanisms of the algorithmic framework, and we prove that, under reasonable assumptions, standard convergence results and some complexity bounds hold for the generalized approach. Moreover, we prove that popular search directions can indeed be soundly used within the framework. Then, we provide a completely novel type of convergence result, concerning the sequence of sets produced by the procedure. In particular, iterate sets are shown to asymptotically approach stationarity for all of their points; the convergence result is accompanied by a worst-case iteration complexity bound; additionally, in finite precision settings, the sets are shown to only be enriched through exploration steps in later iterations, and suitable stopping conditions can be devised. Finally, the results from a large experimental benchmark show that the proposed class of approaches far outperforms state-of-the-art methodologies.<\/jats:p>","DOI":"10.1137\/25m1726856","type":"journal-article","created":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T07:35:21Z","timestamp":1775460921000},"page":"597-625","source":"Crossref","is-referenced-by-count":2,"title":["Effective Front-Descent Algorithms with Convergence Guarantees"],"prefix":"10.1137","volume":"36","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2488-5486","authenticated-orcid":true,"given":"Matteo","family":"Lapucci","sequence":"first","affiliation":[{"name":"Department of Information Engineering, University of Florence, Florence, 50139 Italy."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Pierluigi","family":"Mansueto","sequence":"additional","affiliation":[{"name":"Department of Information Engineering, University of Florence, Florence, 50139 Italy."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Davide","family":"Pucci","sequence":"additional","affiliation":[{"name":"Department of Information Engineering, University of Florence, Florence, 50139 Italy."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2026,4,6]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1007\/s10589-020-00233-8"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1007\/s10589-021-00272-9"},{"key":"ref3","unstructured":"J. Chen, L. Tang, and X. Yang, Barzilai-Borwein Proximal Gradient Methods for Multiobjective Composite Optimization Problems with Improved Linear Convergence, preprint, https:\/\/arxiv.org\/abs\/2306.09797, 2023."},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejco.2021.100008"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1007\/s10589-020-00192-0"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1007\/s10957-020-01781-z"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1137\/10079731X"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1109\/4235.996017"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1007\/s101070100263"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejco.2021.100014"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1137\/08071692X"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1007\/s001860000043"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1080\/10556788.2018.1510928"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1007\/s10589-022-00414-7"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1109\/TCBB.2007.070203"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1109\/TEVC.2005.861417"},{"key":"ref17","unstructured":"Y. Jin, M. Olhofer, and B. Sendhoff, Dynamic weighted aggregation for evolutionary multi-objective optimization: Why does it work and how? in Proceedings of the Genetic and Evolutionary Computation Conference, 2001, pp. 1042\u20131049."},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1109\/TSMCC.2008.919172"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1016\/j.cor.2016.06.021"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1016\/j.orl.2024.107115"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1016\/j.orl.2023.03.001"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1007\/s10589-023-00454-7"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1007\/s12532-022-00231-3"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1016\/j.enconman.2020.113324"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1137\/15M1037810"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1137\/17M1126588"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2007.05.015"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1007\/s10589-023-00510-2"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2013.06.045"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1007\/s10957-022-02072-5"},{"key":"ref31","doi-asserted-by":"publisher","DOI":"10.1016\/j.enbuild.2020.109945"},{"key":"ref32","unstructured":"O. Sch\u00fctze, A. Lara, and C. C. Coello, The directed search method for unconstrained multi-objective optimization problems, in Proceedings of the EVOLVE\u2013A Bridge Between Probability, Set Oriented Numerics, and Evolutionary Computation, 2011, pp. 1\u20134."},{"key":"ref33","unstructured":"Q. Zhang, A. Zhou, S. Zhao, P. N. Suganthan, W. Liu, and S. Tiwari, Multiobjective optimization test instances for the CEC 2009 special session and competition, Technical report, 264, University of Essex, Colchester, UK and Nanyang Technological University, Singapore, Special Session on Performance Assessment of Multi-objective Optimization Algorithms, 2008, pp. 1\u201330."},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0056872"}],"container-title":["SIAM Journal on Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/25M1726856","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T19:11:55Z","timestamp":1787339515000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/25M1726856"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,4,6]]},"references-count":34,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2026,6,30]]}},"alternative-id":["10.1137\/25M1726856"],"URL":"https:\/\/doi.org\/10.1137\/25m1726856","relation":{},"ISSN":["1052-6234","1095-7189"],"issn-type":[{"value":"1052-6234","type":"print"},{"value":"1095-7189","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,4,6]]}}}