{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T20:57:40Z","timestamp":1775077060530,"version":"3.50.1"},"reference-count":46,"publisher":"EDP Sciences","issue":"4","license":[{"start":{"date-parts":[[2023,9,18]],"date-time":"2023-09-18T00:00:00Z","timestamp":1694995200000},"content-version":"vor","delay-in-days":79,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["RAIRO-Oper. Res."],"accepted":{"date-parts":[[2023,7,13]]},"published-print":{"date-parts":[[2023,7]]},"abstract":"<jats:p>We introduce a proximal algorithm using quasidistances for multiobjective minimization problems with quasiconvex functions defined in arbitrary Riemannian manifolds. The reason of using quasidistances instead of the classical Riemannian distance comes from the applications in economy, computer science and behavioral sciences, where the quasidistances represent a non symmetric measure. Under some appropriate assumptions on the problem and using tools of Riemannian geometry we prove that accumulation points of the sequence generated by the algorithm satisfy the critical condition of Pareto-Clarke. If the functions are convex then these points are Pareto efficient solutions.<\/jats:p>","DOI":"10.1051\/ro\/2023101","type":"journal-article","created":{"date-parts":[[2023,7,18]],"date-time":"2023-07-18T08:04:25Z","timestamp":1689667465000},"page":"2301-2314","source":"Crossref","is-referenced-by-count":3,"title":["Proximal algorithm with quasidistances for multiobjective quasiconvex minimization in Riemannian manifolds"],"prefix":"10.1051","volume":"57","author":[{"given":"Erik Alex Papa","family":"Quiroz","sequence":"first","affiliation":[]},{"given":"Rog\u00e9rio Azevedo","family":"Rocha","sequence":"additional","affiliation":[]},{"given":"Paulo","family":"Oliveira","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2229-0523","authenticated-orcid":false,"given":"Ronaldo","family":"Greg\u00f3rio","sequence":"additional","affiliation":[]}],"member":"250","published-online":{"date-parts":[[2023,9,18]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","unstructured":"Absil P.-A., Mahony R. and Sepulchre R., Optimization Algorithms on Matrix Manifolds. Princeton University Press, Princeton, NJ (2009).","DOI":"10.1515\/9781400830244"},{"key":"R2","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1007\/s10898-015-0367-3","volume":"64","author":"Apolinario","year":"2016","journal-title":"J. Global Optim."},{"key":"R3","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1007\/s11228-010-0139-7","volume":"19","author":"Attouch","year":"2011","journal-title":"Set-Valued Var. Anal."},{"key":"R4","doi-asserted-by":"crossref","first-page":"304","DOI":"10.1016\/j.jfa.2004.10.008","volume":"220","author":"Azagra","year":"2005","journal-title":"J. Funct. Anal."},{"key":"R5","doi-asserted-by":"crossref","first-page":"290","DOI":"10.1007\/s10957-014-0569-8","volume":"164","author":"Bao","year":"2015","journal-title":"J. Optim. Theory App."},{"key":"R6","doi-asserted-by":"crossref","first-page":"397","DOI":"10.1007\/s40305-016-0133-3","volume":"4","author":"Baygorrea","year":"2016","journal-title":"J. Oper. Res. Soc. Chin."},{"key":"R7","doi-asserted-by":"crossref","first-page":"564","DOI":"10.1016\/j.na.2010.03.057","volume":"73","author":"Bento","year":"2010","journal-title":"Nonlinear Anal."},{"key":"R8","doi-asserted-by":"crossref","first-page":"557","DOI":"10.1007\/s11228-014-0279-2","volume":"22","author":"Bento","year":"2014","journal-title":"Set-Valued Var. Anal."},{"key":"R9","doi-asserted-by":"crossref","first-page":"743","DOI":"10.1007\/s10957-015-0861-2","volume":"168","author":"Bento","year":"2016","journal-title":"J. Optim. Theory App."},{"key":"R10","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1016\/j.orl.2017.10.017","volume":"46","author":"Bento","year":"2018","journal-title":"Oper. Res. Lett."},{"key":"R11","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1007\/s10957-018-1330-5","volume":"179","author":"Bento","year":"2018","journal-title":"J. Optim. Theory App."},{"key":"R12","doi-asserted-by":"crossref","first-page":"556","DOI":"10.1137\/060670080","volume":"18","author":"Bolte","year":"2007","journal-title":"SIAM J. Optim."},{"key":"R13","doi-asserted-by":"crossref","first-page":"953","DOI":"10.1137\/S1052623403429093","volume":"15","author":"Bonnel","year":"2005","journal-title":"SIAM J. Optim."},{"key":"R14","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.ejor.2006.09.070","volume":"183","author":"Ceng","year":"2007","journal-title":"Eur. J. Oper. Res."},{"key":"R15","doi-asserted-by":"crossref","first-page":"935","DOI":"10.1080\/00036811.2010.483428","volume":"90","author":"Chen","year":"2011","journal-title":"Appl. Anal."},{"key":"R16","first-page":"524698","volume":"2014","author":"Chen","year":"2014","journal-title":"J. Appl. Math."},{"key":"R17","doi-asserted-by":"crossref","first-page":"843","DOI":"10.1080\/01630563.2011.587072","volume":"32","author":"Chuong","year":"2011","journal-title":"Numer. Funct. Anal. Opt."},{"key":"R18","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1017\/S0960129506005111","volume":"16","author":"Concilio","year":"2006","journal-title":"Math. Struct. Comput. Sci."},{"key":"R19","first-page":"395","volume":"20","author":"Da Cruz Neto","year":"2013","journal-title":"J. Convex Anal."},{"key":"R20","doi-asserted-by":"crossref","unstructured":"Do Carmo M.P., Riemannian Geometry. Bikhausen, Boston (1992).","DOI":"10.1007\/978-1-4757-2201-7"},{"key":"R21","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1080\/02331930290019413","volume":"51","author":"Ferreira","year":"2002","journal-title":"Optimization"},{"key":"R22","doi-asserted-by":"crossref","first-page":"660","DOI":"10.1016\/j.matpur.2013.10.002","volume":"101","author":"Kristaly","year":"2014","journal-title":"J. Math. Pures App."},{"key":"R23","first-page":"154","volume":"4","author":"Martinet","year":"1970","journal-title":"Revue Fracaise d\u2019informatique et Recherche Operationelle"},{"key":"R24","doi-asserted-by":"crossref","unstructured":"Mordukhovich B.S., Variational Analysis and Generalized Differentiation I, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Vol. 330. Springer, Berlin (2006).","DOI":"10.1007\/3-540-31246-3"},{"key":"R25","doi-asserted-by":"crossref","first-page":"1383","DOI":"10.1080\/02331934.2011.564623","volume":"61","author":"Moreno","year":"2012","journal-title":"Optimization"},{"key":"R26","doi-asserted-by":"crossref","first-page":"116","DOI":"10.1016\/0022-247X(82)90180-9","volume":"88","author":"Motreanu","year":"1982","journal-title":"J. Math. Anal. App."},{"key":"R27","first-page":"46","volume":"16","author":"Papa Quiroz","year":"2009","journal-title":"J. Convex Anal."},{"key":"R28","first-page":"483","volume":"18","author":"Papa Quiroz","year":"2012","journal-title":"ESAIM: Control Optim. Calculus Var."},{"key":"R29","doi-asserted-by":"crossref","first-page":"1028","DOI":"10.1007\/s10957-019-01582-z","volume":"183","author":"Papa Quiroz","year":"2019","journal-title":"J. Optim. Theory App."},{"key":"R30","doi-asserted-by":"crossref","first-page":"879","DOI":"10.1007\/s10957-020-01725-7","volume":"186","author":"Papa Quiroz","year":"2020","journal-title":"J. Optim. Theory App."},{"key":"R31","doi-asserted-by":"crossref","unstructured":"Papa Quiroz E.A., Baygorrea N., Maculan N., Clarke Subdiferential, Pareto-Clarke critical points and descent directions to multiobjective optimization on Hadamard manifolds, in MCO 2021: Modelling, Computation and Optimization in Information Systems and Management Sciences. Springer International Publishing, Cham (2021) 182\u2013192.","DOI":"10.1007\/978-3-030-92666-3_16"},{"key":"R32","doi-asserted-by":"crossref","unstructured":"Rapcs\u00e1k T., Smooth Nonlinear Optimization in \u211dn. Kluwer Academic Publishers (1997).","DOI":"10.1007\/978-1-4615-6357-0"},{"key":"R33","doi-asserted-by":"crossref","first-page":"964","DOI":"10.1007\/s10957-016-1005-z","volume":"171","author":"Rocha","year":"2016","journal-title":"J. Optim. Theory App."},{"key":"R34","doi-asserted-by":"crossref","first-page":"877","DOI":"10.1137\/0314056","volume":"14","author":"Rockafellar","year":"1976","journal-title":"SIAM J. Control Optim."},{"key":"R35","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1016\/S0022-247X(03)00285-3","volume":"283","author":"Romaguera","year":"2003","journal-title":"J. Math. Anal. Appl."},{"key":"R36","doi-asserted-by":"crossref","unstructured":"Sakai T., Riemannian Geometry. American Mathematical Society, Providence, RI (1996).","DOI":"10.1090\/mmono\/149"},{"key":"R37","unstructured":"Soubeyran A., Variational rationality, a theory of individual stability and change: worthwhile and ambidextry behaviors. GREQAM, Aix Marseille University. Preprint (2009)."},{"key":"R38","unstructured":"Soubeyran A., Variational rationality and the unsatisfied man: routines and the course pursuit between aspirations, capabilities and beliefs. GREQAM, Aix Marseille University. Preprint (2010)."},{"key":"R39","unstructured":"Soubeyran A., A theory of worthwhile stay and change approach-avoidance transitions ending in traps. GREQAM-AMSE, Aix Marseille University. Preprint (2016)."},{"key":"R40","unstructured":"Soubeyran A., Variational rationality: towards a grand theory of motivation driven by worthwhile moves. AMSE, Aix-Marseille University. Preprint (2021)."},{"key":"R41","unstructured":"Soubeyran A., Variational rationality: the concepts of motivation and motivational force. AMSE, Aix-Marseille University. Preprint (2021)."},{"key":"R42","unstructured":"Soubeyran A., Variational rationality. The resolution of goal conflicts via stop and go approach-avoidance dynamics. AMSE, Aix-Marseille University. Preprint (2021c)."},{"key":"R43","unstructured":"Soubeyran A., A general theory of moving goals and intentions as satisficing worthwhile moves. AMSE, Aix-Marseille University. Preprint (2021d)."},{"key":"R44","doi-asserted-by":"crossref","first-page":"745","DOI":"10.1007\/s10957-018-1375-5","volume":"179","author":"Souza","year":"2018","journal-title":"J. Optim. Theory App."},{"key":"R45","doi-asserted-by":"crossref","unstructured":"Udriste C., Convex Function and Optimization Methods on Riemannian Manifolds. Kluwer Academic Publishers (1994).","DOI":"10.1007\/978-94-015-8390-9"},{"key":"R46","doi-asserted-by":"crossref","first-page":"485","DOI":"10.1016\/j.ejor.2011.05.006","volume":"214","author":"Villacorta","year":"2011","journal-title":"Eur. J. Oper. Res."}],"container-title":["RAIRO - Operations Research"],"original-title":[],"link":[{"URL":"https:\/\/www.rairo-ro.org\/10.1051\/ro\/2023101\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,18]],"date-time":"2023-09-18T08:11:40Z","timestamp":1695024700000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.rairo-ro.org\/10.1051\/ro\/2023101"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,7]]},"references-count":46,"journal-issue":{"issue":"4"},"alternative-id":["ro230238"],"URL":"https:\/\/doi.org\/10.1051\/ro\/2023101","relation":{},"ISSN":["0399-0559","2804-7303"],"issn-type":[{"value":"0399-0559","type":"print"},{"value":"2804-7303","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,7]]}}}