{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,13]],"date-time":"2025-05-13T07:06:39Z","timestamp":1747119999580,"version":"3.37.3"},"reference-count":43,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2022,5,7]],"date-time":"2022-05-07T00:00:00Z","timestamp":1651881600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,5,7]],"date-time":"2022-05-07T00:00:00Z","timestamp":1651881600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100002322","name":"Coordena\u00e7\u00e3o de Aperfei\u00e7oamento de Pessoal de N\u00edvel Superior","doi-asserted-by":"publisher","award":["001"],"award-info":[{"award-number":["001"]}],"id":[{"id":"10.13039\/501100002322","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100005285","name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de Goi\u00e1s","doi-asserted-by":"publisher","award":["201710267000532"],"award-info":[{"award-number":["201710267000532"]}],"id":[{"id":"10.13039\/501100005285","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":["310864\/2017-8"],"award-info":[{"award-number":["310864\/2017-8"]}],"id":[{"id":"10.13039\/501100010688","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003593","name":"conselho nacional de desenvolvimento cient\u00edfico e tecnol\u00f3gico","doi-asserted-by":"publisher","award":["308330\/2018-8","423737\/2016-3"],"award-info":[{"award-number":["308330\/2018-8","423737\/2016-3"]}],"id":[{"id":"10.13039\/501100003593","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Ann Oper Res"],"published-print":{"date-parts":[[2022,9]]},"DOI":"10.1007\/s10479-022-04719-y","type":"journal-article","created":{"date-parts":[[2022,5,7]],"date-time":"2022-05-07T11:21:01Z","timestamp":1651922461000},"page":"1425-1443","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Pareto solutions as limits of collective traps: an inexact multiobjective proximal point algorithm"],"prefix":"10.1007","volume":"316","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6983-4132","authenticated-orcid":false,"given":"G. C.","family":"Bento","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7489-6303","authenticated-orcid":false,"given":"J. X.","family":"Cruz Neto","sequence":"additional","affiliation":[]},{"given":"L. V.","family":"Meireles","sequence":"additional","affiliation":[]},{"given":"A.","family":"Soubeyran","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,5,7]]},"reference":[{"key":"4719_CR1","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1007\/s10898-015-0367-3","volume":"64","author":"HCF Apolin\u00e1rio","year":"2016","unstructured":"Apolin\u00e1rio, H. C. F., Papa Quiroz, E. A., & Oliveira, P. R. (2016). A scalarization proximal point method for quasiconvex multiobjective minimization. Journal of Global Optimization, 64, 79\u201396.","journal-title":"Journal of Global Optimization"},{"issue":"3","key":"4719_CR2","doi-asserted-by":"publisher","first-page":"697","DOI":"10.1137\/S1052623403427823","volume":"16","author":"A Auslender","year":"2006","unstructured":"Auslender, A., & Teboulle, M. (2006). Interior gradient and proximal methods for convex and conic optimization. SIAM Journal on Optimization, 16(3), 697\u2013725.","journal-title":"SIAM Journal on Optimization"},{"issue":"1","key":"4719_CR3","doi-asserted-by":"publisher","first-page":"88","DOI":"10.1007\/s10957-011-9984-2","volume":"154","author":"GC Bento","year":"2012","unstructured":"Bento, G. C., Ferreira, O. P., & Oliveira, P. R. (2012). Unconstrained steepest descent method for multicriteria optimization on Riemannian manifolds. Journal of Optimization Theory and Applications, 154(1), 88\u2013107.","journal-title":"Journal of Optimization Theory and Applications"},{"issue":"1","key":"4719_CR4","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1007\/s10957-013-0307-7","volume":"159","author":"GC Bento","year":"2013","unstructured":"Bento, G. C., & Cruz Neto, J. X. (2013). A subgradient method for multiobjective optimization on Riemannian manifolds. Journal of Optimization Theory and Applications, 159(1), 125\u2013137.","journal-title":"Journal of Optimization Theory and Applications"},{"key":"4719_CR5","doi-asserted-by":"publisher","first-page":"557","DOI":"10.1007\/s11228-014-0279-2","volume":"22","author":"GC Bento","year":"2014","unstructured":"Bento, G. C., Cruz Neto, J. X., & Soubeyran, A. (2014). A proximal point-type method for multicriteria optimization. Set-Valued and Variational Analysis, 22, 557\u2013573.","journal-title":"Set-Valued and Variational Analysis"},{"issue":"2","key":"4719_CR6","doi-asserted-by":"publisher","first-page":"1104","DOI":"10.1137\/16M107534X","volume":"28","author":"GC Bento","year":"2018","unstructured":"Bento, G. C., Cruz Neto, J. X., L\u00f3pez, G., Soubeyran, A., & Souza, J. C. O. (2018). The proximal point method for locally Lipschitz functions in multiobjective optimization with application to the compromise problem. SIAM Journal on Optimization, 28(2), 1104\u20131120.","journal-title":"SIAM Journal on Optimization"},{"issue":"1","key":"4719_CR7","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1007\/s10957-018-1330-5","volume":"179","author":"G Bento","year":"2018","unstructured":"Bento, G., Cruz Neto, J. X., & Meireles, L. V. (2018). Proximal point method for locally Lipschitz functions in multiobjective optimization of Hadamard manifolds. Journal of Optimization Theory and Applications, 179(1), 37\u201352.","journal-title":"Journal of Optimization Theory and Applications"},{"key":"4719_CR8","doi-asserted-by":"publisher","DOI":"10.1007\/s10479-021-04052-w","author":"GC Bento","year":"2021","unstructured":"Bento, G. C., Neto, J. C., Soares, P. A., & Soubeyran, A. (2021). A new regularization of equilibrium problems on Hadamard manifolds: Applications to theories of desires. Annals of Operations Research. https:\/\/doi.org\/10.1007\/s10479-021-04052-w.","journal-title":"Annals of Operations Research"},{"issue":"1","key":"4719_CR9","doi-asserted-by":"publisher","first-page":"181","DOI":"10.1007\/s10957-018-1258-9","volume":"177","author":"GC Bento","year":"2018","unstructured":"Bento, G. C., Cruz Neto, J. X., Soubeyran, A., & Sousa J\u00fanior, V. L. (2018). Inexact multi-objective local search proximal algorithms: Application to group dynamic and distributive justice problems. Journal of Optimization Theory and Applications, 177(1), 181\u2013200.","journal-title":"Journal of Optimization Theory and Applications"},{"issue":"1","key":"4719_CR10","doi-asserted-by":"publisher","first-page":"13","DOI":"10.1016\/j.orl.2017.10.017","volume":"46","author":"GC Bento","year":"2018","unstructured":"Bento, G. C., Ferreira, O. P., & Pereira, Y. R. L. (2018). Proximal point method for vector optimization on Hadamard manifolds. Operations Research Letters, 46(1), 13\u201318.","journal-title":"Operations Research Letters"},{"issue":"4","key":"4719_CR11","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. (2005). Proximal methods in vector optimization. SIAM Journal on Optimization, 15(4), 953\u2013970.","journal-title":"SIAM Journal on Optimization"},{"issue":"1","key":"4719_CR12","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.ejor.2006.09.070","volume":"183","author":"LC Ceng","year":"2007","unstructured":"Ceng, L. C., & Yao, J. C. (2007). Approximate proximal methods in vector optimization. European Journal of Operational Research, 183(1), 1\u201319.","journal-title":"European Journal of Operational Research"},{"key":"4719_CR13","doi-asserted-by":"publisher","first-page":"267","DOI":"10.1007\/s10957-010-9667-4","volume":"146","author":"LC Ceng","year":"2010","unstructured":"Ceng, L. C., Mordukhovich, B. S., & Yao, J. C. (2010). Hybrid approximate proximal method with auxiliary variational inequality for vector optimization. Journal of Optimization Theory and Applications, 146, 267\u2013303.","journal-title":"Journal of Optimization Theory and Applications"},{"key":"4719_CR14","unstructured":"Chen, G. Y., Huang, X., & Yang, X. (2005). Vector optimization: Set-valued and variational analysis Lecture notes in economics and mathematical systems (1st ed., Vol. 541). Springer-Verlag."},{"key":"4719_CR15","first-page":"257","volume":"12","author":"TD Choung","year":"2011","unstructured":"Choung, T. D., Mordukhovich, B. S., & Yao, J. C. (2011). Hybrid approximate proximal algorithms for efficient solutions in vector optimization. Journal of Nonlinear and Convex Analysis, 12, 257\u2013286.","journal-title":"Journal of Nonlinear and Convex Analysis"},{"issue":"1","key":"4719_CR16","doi-asserted-by":"publisher","first-page":"187","DOI":"10.1007\/s11117-015-0350-8","volume":"20","author":"TD Chuong","year":"2016","unstructured":"Chuong, T. D., & Kim, D. S. (2016). Approximate solutions of multiobjective optimization problems. Positivity, 20(1), 187\u2013207.","journal-title":"Positivity"},{"key":"4719_CR17","doi-asserted-by":"crossref","unstructured":"Carmo, Do., & M.P.a. (1992). Riemannian geometry. Mathematics: Theory & applications. Birkh\u00e4user Boston Inc.","DOI":"10.1007\/978-1-4757-2201-7"},{"key":"4719_CR18","doi-asserted-by":"publisher","first-page":"281","DOI":"10.1007\/s10898-010-9544-6","volume":"49","author":"R Greg\u00f3rio","year":"2011","unstructured":"Greg\u00f3rio, R., & Oliveira, P. R. (2011). A logarithmic-quadratic proximal point scalarization method for multiobjective programming. Journal of Global Optimization, 49, 281\u2013291.","journal-title":"Journal of Global Optimization"},{"issue":"1","key":"4719_CR19","doi-asserted-by":"publisher","first-page":"111","DOI":"10.1023\/B:JOTA.0000012735.86699.a1","volume":"120","author":"XX Huang","year":"2004","unstructured":"Huang, X. X., & Yang, X. Q. (2004). Duality for multiobjective optimization via nonlinear Lagrangian functions. Journal of Optimization Theory and Applications, 120(1), 111\u2013127.","journal-title":"Journal of Optimization Theory and Applications"},{"key":"4719_CR20","doi-asserted-by":"crossref","unstructured":"Jahn, J. (2004). Vector optimization: Theory, applications, and extensions. Springer.","DOI":"10.1007\/978-3-540-24828-6"},{"issue":"8","key":"4719_CR21","doi-asserted-by":"publisher","first-page":"3687","DOI":"10.1090\/S0002-9947-07-04075-5","volume":"359","author":"YS Ledyaev","year":"2007","unstructured":"Ledyaev, Y. S., & Zhu, Q. J. (2007). Nonsmooth analysis on smooth manifolds. Transactions of the American Mathematical Society, 359(8), 3687\u20133732.","journal-title":"Transactions of the American Mathematical Society"},{"key":"4719_CR22","unstructured":"Lewin, K. (1952). Frontiers in group dynamics. In D. Cartwright (Ed.), (1947) and Field Theory in social Science. Social Science Paperbacks."},{"key":"4719_CR23","unstructured":"Lewin, K. (1959). Group decisions and social change. In T. M. Newcomb & E. L. Hartley (Eds.), Reading in social psychology. Henry Holt."},{"issue":"4","key":"4719_CR24","doi-asserted-by":"publisher","first-page":"1523","DOI":"10.1137\/09075367X","volume":"21","author":"C Li","year":"2011","unstructured":"Li, C., Mordukhovich, B. S., Wang, J., & Yao, J. C. (2011). Weak sharp minima on Riemannian manifolds. SIAM Journal on Optimization, 21(4), 1523\u20131560.","journal-title":"SIAM Journal on Optimization"},{"key":"4719_CR25","doi-asserted-by":"crossref","unstructured":"Loridan, P. (1984). $$\\epsilon $$-solutions in vector minimization problems. Journal of Optimization Theory and Applications, 43(2), 265\u2013276.","DOI":"10.1007\/BF00936165"},{"key":"4719_CR26","doi-asserted-by":"crossref","unstructured":"Luc, D. T. (1989). Theory of vector optimization lecture notes in economics and mathematical systems (Vol. 319). Springer.","DOI":"10.1007\/978-3-642-50280-4"},{"key":"4719_CR27","unstructured":"Meireles, L. V. (2019). Proximal point methods for multiobjective optimization in riemann- ian manifolds (PhD Thesis),"},{"key":"4719_CR28","doi-asserted-by":"publisher","first-page":"451","DOI":"10.1007\/BF00935364","volume":"41","author":"M Minami","year":"1983","unstructured":"Minami, M. (1983). Weak Pareto-optimal necessary conditions in a nondifferentiable multiobjective program on a Banach space. Journal of Optimization Theory and Applications, 41, 451\u2013461.","journal-title":"Journal of Optimization Theory and Applications"},{"issue":"3","key":"4719_CR29","doi-asserted-by":"publisher","first-page":"879","DOI":"10.1007\/s10957-020-01725-7","volume":"186","author":"EAP Quiroz","year":"2020","unstructured":"Quiroz, E. A. P., Cusihuallpa, N. B., & Maculan, N. (2020). Inexact proximal point methods for multiobjective quasiconvex minimization on hadamard manifolds. Journal of Optimization Theory and Applications, 186(3), 879\u2013898.","journal-title":"Journal of Optimization Theory and Applications"},{"key":"4719_CR30","doi-asserted-by":"crossref","unstructured":"Rockafellar, R. T. (1976). Monotone operators and the proximal point algorithm. SIAM Journal on Control and Optimization, 14(5), 877\u2013898.","DOI":"10.1137\/0314056"},{"key":"4719_CR31","doi-asserted-by":"crossref","unstructured":"Sakai, T. (1996). Riemannian geometry, translations of mathematical monographs (Vol. 149). American Mathematical Society.","DOI":"10.1090\/mmono\/149"},{"key":"4719_CR32","doi-asserted-by":"publisher","first-page":"323","DOI":"10.1023\/A:1008777829180","volume":"7","author":"MV Solodov","year":"1999","unstructured":"Solodov, M. V., & Svaiter, B. F. (1999). An inexact hybrid extragradient-proximal point algorithm using the enlargement of a maximal monotone operator. Set-Valued Analysis, 7, 323\u2013345.","journal-title":"Set-Valued Analysis"},{"key":"4719_CR33","unstructured":"Soubeyran, A. (2009). Variational rationality, a theory of individual stability and change: worthwhile and ambidextry behaviors. Preprint. GREQAM: Aix Marseille University."},{"key":"4719_CR34","unstructured":"Soubeyran, A. (2010). Variational rationality and the \u201cunsatisfied man\u201d: routines and the course pursuit between aspirations, capabilities and beliefs. Preprint GREQAM: Aix Marseille University."},{"key":"4719_CR35","unstructured":"Soubeyran, A. (2021). Variational rationality: towards a grand theory of motivation driven by worthwhile moves. Preprint: GREQAM-AMSE, Aix Marseille University."},{"key":"4719_CR36","unstructured":"Soubeyran, A. (2021). Variational rationality: The concepts of motivation and motivational force. Aix-Marseille University."},{"key":"4719_CR37","unstructured":"Soubeyran, A., (2021). Variational rationality. The resolution of goal conflicts via stop and go approach-avoidance dynamics. Preprint. AMSE, Aix-Marseille University"},{"key":"4719_CR38","unstructured":"Soubeyran, A., (2021). Variational rationality. A general theory of moving goals and intentions as satisficing worthwhile moves. Preprint. AMSE, Aix-Marseille University"},{"issue":"3","key":"4719_CR39","doi-asserted-by":"publisher","first-page":"745","DOI":"10.1007\/s10957-018-1375-5","volume":"179","author":"JCO Souza","year":"2018","unstructured":"Souza, J. C. O. (2018). Proximal point methods for Lipschitz functions on Hadamard manifolds: scalar and vectorial cases. Journal of Optimization Theory and Applications, 179(3), 745\u2013760.","journal-title":"Journal of Optimization Theory and Applications"},{"key":"4719_CR40","doi-asserted-by":"crossref","unstructured":"Tang, F. M., & Huang, P. L. (2017). On the convergence rate of a proximal point algorithm for vector function on Hadamard manifolds. Journal of the Operations Research Society of China, 5, 405\u2013417.","DOI":"10.1007\/s40305-016-0146-y"},{"key":"4719_CR41","doi-asserted-by":"crossref","unstructured":"Udriste, C. (1994). Convex functions and optimization methods on riemannian manifolds, mathematics and its applications (Vol. 297). Kluwer Academic Publishers Group.","DOI":"10.1007\/978-94-015-8390-9_3"},{"key":"4719_CR42","doi-asserted-by":"crossref","unstructured":"Villacorta, K. D. V., & Oliveira, P. R. (2011). An interior proximal method in vector optimization. European Journal of Operational Research, 214, 485\u2013492.","DOI":"10.1016\/j.ejor.2011.05.006"},{"key":"4719_CR43","unstructured":"Vinter, R. B. (2000). Optimal control. Birkhauser."}],"container-title":["Annals of Operations Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-022-04719-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10479-022-04719-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-022-04719-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,10,5]],"date-time":"2022-10-05T13:53:59Z","timestamp":1664978039000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10479-022-04719-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,5,7]]},"references-count":43,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2022,9]]}},"alternative-id":["4719"],"URL":"https:\/\/doi.org\/10.1007\/s10479-022-04719-y","relation":{},"ISSN":["0254-5330","1572-9338"],"issn-type":[{"type":"print","value":"0254-5330"},{"type":"electronic","value":"1572-9338"}],"subject":[],"published":{"date-parts":[[2022,5,7]]},"assertion":[{"value":"4 April 2022","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 May 2022","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}