{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T19:20:06Z","timestamp":1775503206332,"version":"3.50.1"},"reference-count":41,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2022,9,16]],"date-time":"2022-09-16T00:00:00Z","timestamp":1663286400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,9,16]],"date-time":"2022-09-16T00:00:00Z","timestamp":1663286400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100003593","name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","doi-asserted-by":"publisher","award":["302666\/2017-6"],"award-info":[{"award-number":["302666\/2017-6"]}],"id":[{"id":"10.13039\/501100003593","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100010688","name":"Instituto Nacional de Ci\u00eancia e Tecnologia da Criosfera","doi-asserted-by":"publisher","award":["408123\/2018-4"],"award-info":[{"award-number":["408123\/2018-4"]}],"id":[{"id":"10.13039\/501100010688","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100010688","name":"Instituto Nacional de Ci\u00eancia e Tecnologia da Criosfera","doi-asserted-by":"publisher","award":["424860\/2018-0"],"award-info":[{"award-number":["424860\/2018-0"]}],"id":[{"id":"10.13039\/501100010688","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comput Optim Appl"],"published-print":{"date-parts":[[2022,11]]},"DOI":"10.1007\/s10589-022-00414-7","type":"journal-article","created":{"date-parts":[[2022,9,16]],"date-time":"2022-09-16T17:03:26Z","timestamp":1663347806000},"page":"403-434","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":37,"title":["Globally convergent Newton-type methods for multiobjective optimization"],"prefix":"10.1007","volume":"83","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9563-1101","authenticated-orcid":false,"given":"M. L. N.","family":"Gon\u00e7alves","sequence":"first","affiliation":[]},{"given":"F. S.","family":"Lima","sequence":"additional","affiliation":[]},{"given":"L. F.","family":"Prudente","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,9,16]]},"reference":[{"key":"414_CR1","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898719604","volume-title":"LAPACK Users\u2019 Guide","author":"E Anderson","year":"1999","unstructured":"Anderson, E., Bai, Z., Bischof, C., Blackford, S., Demmel, J., Dongarra, J., Du Croz, J., Greenbaum, A., Hammarling, S., McKenney, A., Sorensen, D.: LAPACK Users\u2019 Guide, 3rd edn. SIAM, Philadelphia (1999)","edition":"3"},{"issue":"11","key":"414_CR2","doi-asserted-by":"publisher","first-page":"2289","DOI":"10.1080\/02331934.2014.947500","volume":"64","author":"MA Ansary","year":"2015","unstructured":"Ansary, M.A., Panda, G.: A modified Quasi-Newton method for vector optimization problem. Optimization 64(11), 2289\u20132306 (2015)","journal-title":"Optimization"},{"key":"414_CR3","doi-asserted-by":"publisher","first-page":"741","DOI":"10.1007\/s10589-020-00260-5","volume":"78","author":"PB Assun\u00e7\u00e3o","year":"2021","unstructured":"Assun\u00e7\u00e3o, P.B., Ferreira, O.P., Prudente, L.F.: Conditional gradient method for multiobjective optimization. Comput. Optim. Appl. 78, 741\u2013768 (2021). https:\/\/doi.org\/10.1007\/s10589-020-00260-5","journal-title":"Comput. Optim. Appl."},{"key":"414_CR4","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611973365","volume-title":"Practical Augmented Lagrangian Methods for Constrained Optimization","author":"E Birgin","year":"2014","unstructured":"Birgin, E., Martinez, J.: Practical Augmented Lagrangian Methods for Constrained Optimization. SIAM, Philadelphia (2014)"},{"issue":"4","key":"414_CR5","doi-asserted-by":"publisher","first-page":"953","DOI":"10.1137\/S1052623403429093","volume":"15","author":"H Bonnel","year":"2005","unstructured":"Bonnel, H., Iusem, A.N., Svaiter, B.F.: Proximal methods in vector optimization. SIAM J. Optim. 15(4), 953\u2013970 (2005)","journal-title":"SIAM J. Optim."},{"issue":"3","key":"414_CR6","doi-asserted-by":"publisher","first-page":"1109","DOI":"10.1137\/10079731X","volume":"21","author":"AL Cust\u00f3dio","year":"2011","unstructured":"Cust\u00f3dio, A.L., Madeira, J.F.A., Vaz, A.I.F., Vicente, L.N.: Direct multisearch for multiobjective optimization. SIAM J. Optim. 21(3), 1109\u20131140 (2011). https:\/\/doi.org\/10.1137\/10079731X","journal-title":"SIAM J. Optim."},{"issue":"3","key":"414_CR7","doi-asserted-by":"publisher","first-page":"693","DOI":"10.1137\/S1052623401383455","volume":"13","author":"YH Dai","year":"2002","unstructured":"Dai, Y.H.: Convergence properties of the BFGS algorithm. SIAM J. Optim. 13(3), 693\u2013701 (2002)","journal-title":"SIAM J. Optim."},{"issue":"1\u20132","key":"414_CR8","doi-asserted-by":"publisher","first-page":"501","DOI":"10.1007\/s10107-012-0522-2","volume":"138","author":"YH Dai","year":"2013","unstructured":"Dai, Y.H.: A perfect example for the BFGS method. Math. Program. 138(1\u20132), 501\u2013530 (2013)","journal-title":"Math. Program."},{"issue":"3","key":"414_CR9","doi-asserted-by":"publisher","first-page":"631","DOI":"10.1137\/S1052623496307510","volume":"8","author":"I Das","year":"1998","unstructured":"Das, I., Dennis, J.: Normal-boundary intersection: a new method for generating the Pareto surface in nonlinear multicriteria optimization problems. SIAM J. Optim. 8(3), 631\u2013657 (1998)","journal-title":"SIAM J. Optim."},{"issue":"2","key":"414_CR10","doi-asserted-by":"publisher","first-page":"201","DOI":"10.1007\/s101070100263","volume":"91","author":"ED Dolan","year":"2002","unstructured":"Dolan, E.D., Mor\u00e9, J.J.: Benchmarking optimization software with performance profiles. Math. Program. 91(2), 201\u2013213 (2002)","journal-title":"Math. Program."},{"issue":"6","key":"414_CR11","doi-asserted-by":"publisher","first-page":"1365","DOI":"10.1007\/s11590-018-1353-8","volume":"13","author":"NS Fazzio","year":"2019","unstructured":"Fazzio, N.S., Schuverdt, M.L.: Convergence analysis of a nonmonotone projected gradient method for multiobjective optimization problems. Optim. Lett. 13(6), 1365\u20131379 (2019)","journal-title":"Optim. Lett."},{"issue":"2","key":"414_CR12","doi-asserted-by":"publisher","first-page":"602","DOI":"10.1137\/08071692X","volume":"20","author":"J Fliege","year":"2009","unstructured":"Fliege, J., Gra\u00f1a Drummond, L.M., Svaiter, B.F.: Newton\u2019s method for multiobjective optimization. SIAM J. Optim. 20(2), 602\u2013626 (2009)","journal-title":"SIAM J. Optim."},{"issue":"3","key":"414_CR13","doi-asserted-by":"publisher","first-page":"479","DOI":"10.1007\/s001860000043","volume":"51","author":"J Fliege","year":"2000","unstructured":"Fliege, J., Svaiter, B.F.: Steepest descent methods for multicriteria optimization. Math. Method. Oper. Res. 51(3), 479\u2013494 (2000)","journal-title":"Math. Method. Oper. Res."},{"issue":"3","key":"414_CR14","doi-asserted-by":"publisher","first-page":"473","DOI":"10.1007\/s10589-012-9501-z","volume":"54","author":"EH Fukuda","year":"2013","unstructured":"Fukuda, E.H., Gra\u00f1a Drummond, L.M.: Inexact projected gradient method for vector optimization. Comput. Optim. Appl. 54(3), 473\u2013493 (2013)","journal-title":"Comput. Optim. Appl."},{"issue":"3","key":"414_CR15","doi-asserted-by":"publisher","first-page":"618","DOI":"10.1016\/0022-247X(68)90201-1","volume":"22","author":"AM Geoffrion","year":"1968","unstructured":"Geoffrion, A.M.: Proper efficiency and the theory of vector maximization. J. Math. Anal. Appl. 22(3), 618\u2013630 (1968)","journal-title":"J. Math. Anal. Appl."},{"issue":"3","key":"414_CR16","doi-asserted-by":"publisher","first-page":"889","DOI":"10.1007\/s10589-019-00146-1","volume":"76","author":"MLN Gon\u00e7alves","year":"2020","unstructured":"Gon\u00e7alves, M.L.N., Prudente, L.F.: On the extension of the Hager\u2013Zhang conjugate gradient method for vector optimization. Comput. Optim. Appl. 76(3), 889\u2013916 (2020)","journal-title":"Comput. Optim. Appl."},{"issue":"1","key":"414_CR17","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1023\/B:COAP.0000018877.86161.8b","volume":"28","author":"LM Gra\u00f1a Drummond","year":"2004","unstructured":"Gra\u00f1a Drummond, L.M., Iusem, A.N.: A projected gradient method for vector optimization problems. Comput. Optim. Appl. 28(1), 5\u201329 (2004)","journal-title":"Comput. Optim. Appl."},{"issue":"5","key":"414_CR18","doi-asserted-by":"publisher","first-page":"661","DOI":"10.1080\/02331934.2012.693082","volume":"63","author":"LM Gra\u00f1a Drummond","year":"2014","unstructured":"Gra\u00f1a Drummond, L.M., Raupp, F.M.P., Svaiter, B.F.: A quadratically convergent Newton method for vector optimization. Optimization 63(5), 661\u2013677 (2014)","journal-title":"Optimization"},{"issue":"2","key":"414_CR19","doi-asserted-by":"publisher","first-page":"395","DOI":"10.1016\/j.cam.2004.06.018","volume":"175","author":"LM Gra\u00f1a Drummond","year":"2005","unstructured":"Gra\u00f1a Drummond, L.M., Svaiter, B.F.: A steepest descent method for vector optimization. J. Comput. Appl. Math. 175(2), 395\u2013414 (2005)","journal-title":"J. Comput. Appl. Math."},{"issue":"3","key":"414_CR20","doi-asserted-by":"publisher","first-page":"557","DOI":"10.1023\/A:1017536311488","volume":"110","author":"C Hillermeier","year":"2001","unstructured":"Hillermeier, C.: Generalized homotopy approach to multiobjective optimization. J. Optimiz. Theory App. 110(3), 557\u2013583 (2001)","journal-title":"J. Optimiz. Theory App."},{"issue":"5","key":"414_CR21","doi-asserted-by":"publisher","first-page":"477","DOI":"10.1109\/TEVC.2005.861417","volume":"10","author":"S Huband","year":"2006","unstructured":"Huband, S., Hingston, P., Barone, L., While, L.: A review of multiobjective test problems and a scalable test problem toolkit. IEEE Trans. Evolut. Comput. 10(5), 477\u2013506 (2006)","journal-title":"IEEE Trans. Evolut. Comput."},{"key":"414_CR22","unstructured":"Jin, Y., Olhofer, M., Sendhoff, B.: Dynamic weighted aggregation for evolutionary multi-objective optimization: Why does it work and how? In: Proceedings of the 3rd Annual Conference on Genetic and Evolutionary Computation, GECCO\u201901, pp. 1042-1049. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2001)"},{"issue":"2","key":"414_CR23","doi-asserted-by":"publisher","first-page":"149","DOI":"10.1007\/s00158-004-0465-1","volume":"29","author":"I Kim","year":"2005","unstructured":"Kim, I., de Weck, O.: Adaptive weighted-sum method for bi-objective optimization: Pareto front generation. Struct. Multidiscip. Optim. 29(2), 149\u2013158 (2005)","journal-title":"Struct. Multidiscip. Optim."},{"issue":"3","key":"414_CR24","doi-asserted-by":"publisher","first-page":"263","DOI":"10.1162\/106365602760234108","volume":"10","author":"M Laumanns","year":"2002","unstructured":"Laumanns, M., Thiele, L., Deb, K., Zitzler, E.: Combining convergence and diversity in evolutionary multiobjective optimization. Evol. Comput. 10(3), 263\u2013282 (2002)","journal-title":"Evol. Comput."},{"issue":"2","key":"414_CR25","doi-asserted-by":"publisher","first-page":"463","DOI":"10.1137\/100784746","volume":"21","author":"A Lovison","year":"2011","unstructured":"Lovison, A.: Singular continuation: generating piecewise linear approximations to Pareto sets via global analysis. SIAM J. Optim. 21(2), 463\u2013490 (2011)","journal-title":"SIAM J. Optim."},{"key":"414_CR26","doi-asserted-by":"crossref","unstructured":"Luc, D.T.: Theory of vector optimization. Lectures Notes in economics and mathematical systems, Vol. 319 (1989)","DOI":"10.1007\/978-3-642-50280-4"},{"issue":"3","key":"414_CR27","doi-asserted-by":"publisher","first-page":"2690","DOI":"10.1137\/17M1126588","volume":"28","author":"LR Lucambio P\u00e9rez","year":"2018","unstructured":"Lucambio P\u00e9rez, L.R., Prudente, L.F.: Nonlinear conjugate gradient methods for vector optimization. SIAM J. Optim. 28(3), 2690\u20132720 (2018)","journal-title":"SIAM J. Optim."},{"issue":"4","key":"414_CR28","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1145\/3342104","volume":"45","author":"LR Lucambio P\u00e9rez","year":"2019","unstructured":"Lucambio P\u00e9rez, L.R., Prudente, L.F.: A Wolfe line search algorithm for vector optimization. ACM Trans. Math. Softw. 45(4), 23 (2019)","journal-title":"ACM Trans. Math. Softw."},{"issue":"1","key":"414_CR29","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1007\/s10107-003-0421-7","volume":"99","author":"WF Mascarenhas","year":"2004","unstructured":"Mascarenhas, W.F.: The BFGS method with exact line searches fails for non-convex objective functions. Math. Program. 99(1), 49\u201361 (2004)","journal-title":"Math. Program."},{"issue":"1","key":"414_CR30","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1590\/S0101-82052007000100006","volume":"26","author":"WF Mascarenhas","year":"2007","unstructured":"Mascarenhas, W.F.: On the divergence of line search methods. Comput. Appl. Math. 26(1), 129\u2013169 (2007)","journal-title":"Comput. Appl. Math."},{"issue":"3","key":"414_CR31","doi-asserted-by":"publisher","first-page":"662","DOI":"10.1016\/j.ejor.2007.05.015","volume":"188","author":"E Miglierina","year":"2008","unstructured":"Miglierina, E., Molho, E., Recchioni, M.: Box-constrained multi-objective optimization: a gradient-like method without a priori scalarization. Eur. J. Oper. Res. 188(3), 662\u2013682 (2008)","journal-title":"Eur. J. Oper. Res."},{"key":"414_CR32","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1007\/s10898-019-00802-0","volume":"75","author":"K Mita","year":"2019","unstructured":"Mita, K., Fukuda, E.H., Yamashita, N.: Nonmonotone line searches for unconstrained multiobjective optimization problems. J. Global Optim. 75, 63\u201390 (2019)","journal-title":"J. Global Optim."},{"issue":"1","key":"414_CR33","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1145\/355934.355936","volume":"7","author":"JJ Mor\u00e9","year":"1981","unstructured":"Mor\u00e9, J.J., Garbow, B.S., Hillstrom, K.E.: Testing unconstrained optimization software. ACM Trans. Math. Softw. 7(1), 17\u201341 (1981)","journal-title":"ACM Trans. Math. Softw."},{"key":"414_CR34","unstructured":"Nocedal, J., Wright, S.: Numerical optimization. Springer (2006)"},{"key":"414_CR35","doi-asserted-by":"publisher","first-page":"765","DOI":"10.1016\/j.cam.2013.06.045","volume":"255","author":"Z Povalej","year":"2014","unstructured":"Povalej, Z.: Quasi-Newton method for multiobjective optimization. J. Comput. Appl. Math. 255, 765\u2013777 (2014)","journal-title":"J. Comput. Appl. Math."},{"key":"414_CR36","doi-asserted-by":"publisher","first-page":"513","DOI":"10.1007\/11844297_52","volume-title":"Parallel Problem Solving from Nature - PPSN IX","author":"M Preuss","year":"2006","unstructured":"Preuss, M., Naujoks, B., Rudolph, G.: Pareto set and EMOA behavior for simple multimodal multiobjective functions. In: Runarsson, T.P., Beyer, H.G., Burke, E., Merelo-Guerv\u00f3s, J.J., Whitley, L.D., Yao, X. (eds.) Parallel Problem Solving from Nature - PPSN IX, pp. 513\u2013522. Springer, Berlin (2006)"},{"issue":"2","key":"414_CR37","doi-asserted-by":"publisher","first-page":"356","DOI":"10.1016\/j.ejor.2017.05.027","volume":"263","author":"S Qu","year":"2017","unstructured":"Qu, S., Ji, Y., Jiang, J., Zhang, Q.: Nonmonotone gradient methods for vector optimization with a portfolio optimization application. Eur. J. Oper. Res. 263(2), 356\u2013366 (2017)","journal-title":"Eur. J. Oper. Res."},{"issue":"4","key":"414_CR38","doi-asserted-by":"publisher","first-page":"559","DOI":"10.1007\/s10898-007-9265-7","volume":"41","author":"O Sch\u00fctze","year":"2008","unstructured":"Sch\u00fctze, O., Laumanns, M., Coello Coello, C.A., Dellnitz, M., Talbi, E.G.: Convergence of stochastic search algorithms to finite size Pareto set approximations. J. Global Optim. 41(4), 559\u2013577 (2008)","journal-title":"J. Global Optim."},{"issue":"4","key":"414_CR39","doi-asserted-by":"publisher","first-page":"430","DOI":"10.1016\/j.orl.2018.05.008","volume":"46","author":"BF Svaiter","year":"2018","unstructured":"Svaiter, B.F.: The multiobjective steepest descent direction is not Lipschitz continuous, but is H\u00f6lder continuous. Oper. Res. Lett. 46(4), 430\u2013433 (2018)","journal-title":"Oper. Res. Lett."},{"key":"414_CR40","unstructured":"Toint, P.L.: Test problems for partially separable optimization and results for the routine PSPMIN. The University of Namur, Department of Mathematics, Belgium, Tech. Rep (1983)"},{"key":"414_CR41","doi-asserted-by":"crossref","unstructured":"Wang, J., Hu, Y., Wai, Yu., C.K., Li, C., Yang, X.: Extended Newton methods for multiobjective optimization: majorizing function technique and convergence analysis. SIAM J. Optim. 29(3), 2388\u20132421 (2019)","DOI":"10.1137\/18M1191737"}],"container-title":["Computational Optimization and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-022-00414-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10589-022-00414-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-022-00414-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,27]],"date-time":"2023-11-27T02:43:17Z","timestamp":1701052997000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10589-022-00414-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,9,16]]},"references-count":41,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2022,11]]}},"alternative-id":["414"],"URL":"https:\/\/doi.org\/10.1007\/s10589-022-00414-7","relation":{},"ISSN":["0926-6003","1573-2894"],"issn-type":[{"value":"0926-6003","type":"print"},{"value":"1573-2894","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,9,16]]},"assertion":[{"value":"10 February 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"1 September 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 September 2022","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflicts of interest"}}]}}