{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,4]],"date-time":"2026-06-04T01:14:09Z","timestamp":1780535649033,"version":"3.54.1"},"reference-count":44,"publisher":"Informa UK Limited","issue":"3","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12271113"],"award-info":[{"award-number":["12271113"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12171106"],"award-info":[{"award-number":["12171106"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12061013"],"award-info":[{"award-number":["12061013"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Guangxi Ba Gui Scholars","award":["GXR-6BG2424008"],"award-info":[{"award-number":["GXR-6BG2424008"]}]}],"content-domain":{"domain":["www.tandfonline.com"],"crossmark-restriction":true},"short-container-title":["Optimization Methods and Software"],"published-print":{"date-parts":[[2025,5,4]]},"DOI":"10.1080\/10556788.2024.2436173","type":"journal-article","created":{"date-parts":[[2024,12,23]],"date-time":"2024-12-23T14:56:26Z","timestamp":1734965786000},"page":"487-508","update-policy":"https:\/\/doi.org\/10.1080\/tandf_crossmark_01","source":"Crossref","is-referenced-by-count":1,"title":["An implementable descent method for nonsmooth multiobjective optimization on Riemannian manifolds"],"prefix":"10.1080","volume":"40","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1649-2217","authenticated-orcid":false,"given":"Chunming","family":"Tang","sequence":"first","affiliation":[{"name":"Guangxi University","place":["Nanning, People's Republic of China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hao","family":"He","sequence":"additional","affiliation":[{"name":"Guangxi University","place":["Nanning, People's Republic of China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8048-7397","authenticated-orcid":false,"given":"Jinbao","family":"Jian","sequence":"additional","affiliation":[{"name":"College of Mathematics and Physics, Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis, Center for Applied Mathematics and Artificial Intelligence, Guangxi Minzu University","place":["Nanning, People's Republic of China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Miantao","family":"Chao","sequence":"additional","affiliation":[{"name":"Guangxi University","place":["Nanning, People's Republic of China"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"301","published-online":{"date-parts":[[2024,12,23]]},"reference":[{"key":"e_1_3_4_2_1","doi-asserted-by":"publisher","DOI":"10.1007\/1-84628-137-7"},{"key":"e_1_3_4_3_1","doi-asserted-by":"publisher","DOI":"10.1515\/9781400830244"},{"key":"e_1_3_4_4_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2014.09.001"},{"key":"e_1_3_4_5_1","doi-asserted-by":"publisher","DOI":"10.1287\/opre.37.1.118"},{"key":"e_1_3_4_6_1","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623403429093"},{"key":"e_1_3_4_7_1","doi-asserted-by":"publisher","DOI":"10.1137\/030601296"},{"key":"e_1_3_4_8_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10957-011-9921-4"},{"key":"e_1_3_4_9_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2010.03.057"},{"key":"e_1_3_4_10_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10957-011-9984-2"},{"key":"e_1_3_4_11_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10957-013-0307-7"},{"key":"e_1_3_4_12_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10957-013-0305-9"},{"key":"e_1_3_4_13_1","doi-asserted-by":"publisher","DOI":"10.1137\/16M107534X"},{"key":"e_1_3_4_14_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10957-018-1330-5"},{"key":"e_1_3_4_15_1","doi-asserted-by":"publisher","DOI":"10.1017\/9781009166164"},{"key":"e_1_3_4_16_1","volume-title":"Optimization and Nonsmooth Analysis","author":"Clarke F.","year":"1983","unstructured":"F. Clarke, Optimization and Nonsmooth Analysis, Society for Industrial and Applied Mathematics, New York, 1983."},{"key":"e_1_3_4_17_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-85729-652-8_1"},{"key":"e_1_3_4_18_1","volume-title":"Multicriteria Optimization","author":"Ehrgott M.","year":"2005","unstructured":"M. Ehrgott, Multicriteria Optimization, Springer, Berlin, 2005."},{"key":"e_1_3_4_19_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00158-006-0078-y"},{"key":"e_1_3_4_20_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10957-020-01785-9"},{"key":"e_1_3_4_21_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10957-022-02142-8"},{"key":"e_1_3_4_22_1","doi-asserted-by":"publisher","DOI":"10.1007\/s001860000043"},{"key":"e_1_3_4_23_1","doi-asserted-by":"publisher","DOI":"10.1007\/PL00013342"},{"key":"e_1_3_4_24_1","doi-asserted-by":"publisher","DOI":"10.1137\/08071692X"},{"key":"e_1_3_4_25_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.neuroimage.2008.10.052"},{"key":"e_1_3_4_26_1","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(68)90201-1"},{"key":"e_1_3_4_27_1","doi-asserted-by":"publisher","DOI":"10.1016\/0377-2217(92)90284-G"},{"key":"e_1_3_4_28_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10957-020-01803-w"},{"key":"e_1_3_4_29_1","unstructured":"B. Gebken Computation and analysis of Pareto critical sets in smooth and nonsmooth multiobjective optimization Ph.D. thesis. Paderborn University 2022."},{"key":"e_1_3_4_30_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2011.02.023"},{"key":"e_1_3_4_31_1","unstructured":"W. Huang Optimization Algorithms on Riemannian Manifolds with Applications Ph.D. thesis Department of Mathematics Florida State University Tallahassee FL 2013."},{"key":"e_1_3_4_32_1","doi-asserted-by":"publisher","DOI":"10.1137\/140955483"},{"key":"e_1_3_4_33_1","doi-asserted-by":"publisher","DOI":"10.1137\/16M1069298"},{"key":"e_1_3_4_34_1","doi-asserted-by":"publisher","DOI":"10.1137\/16M1108145"},{"key":"e_1_3_4_35_1","doi-asserted-by":"publisher","DOI":"10.1007\/s40305-020-00295-9"},{"key":"e_1_3_4_36_1","doi-asserted-by":"publisher","DOI":"10.1093\/imanum\/drab091"},{"key":"e_1_3_4_37_1","doi-asserted-by":"publisher","DOI":"10.1016\/0377-2217(92)90228-2"},{"key":"e_1_3_4_38_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10957-012-0024-7"},{"key":"e_1_3_4_39_1","first-page":"333","volume-title":"On Nonsmooth Multiobjective Optimality Conditions with Generalized Convexities","author":"M\u00e4kel\u00e4 M.M.","year":"2014","unstructured":"M.M. M\u00e4kel\u00e4, V.P. Eronen, and N. Karmitsa.\u00a0On Nonsmooth Multiobjective Optimality Conditions with Generalized Convexities, in Optimization in Science and Engineering, ed. by T.M. Rassias, C.A. Floudas, S. Butenko, Springer, New York, 2014. pp. 333\u2013357."},{"key":"e_1_3_4_40_1","series-title":"in Mathematical Modeling and Optimization of Complex Structures, ed. by P. Neittaanm\u00e4ki, S. Repin, T. Tuovinen","first-page":"191","volume-title":"Proximal Bundle Method for Nonsmooth and Nonconvex Multiobjective Optimization","author":"M\u00e4kel\u00e4 M.M.","year":"2016","unstructured":"M.M. M\u00e4kel\u00e4, N. Karmitsa, and O. Wilppu, Proximal Bundle Method for Nonsmooth and Nonconvex Multiobjective Optimization, in Mathematical Modeling and Optimization of Complex Structures, ed. by P. Neittaanm\u00e4ki, S. Repin, T. Tuovinen. Springer, Cham, 2016, pp. 191\u2013204."},{"key":"e_1_3_4_41_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2013.06.045"},{"key":"e_1_3_4_42_1","volume-title":"Theory of Multiobjective Optimization","author":"Sawaragi Y.","year":"1985","unstructured":"Y. Sawaragi, H. Nakayama, and T. Tanino, Theory of Multiobjective Optimization, Elsevier, Orlando, 1985."},{"key":"e_1_3_4_43_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-62391-3"},{"key":"e_1_3_4_44_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.2517-6161.1996.tb02080.x"},{"key":"e_1_3_4_45_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10589-016-9883-4"}],"container-title":["Optimization Methods and Software"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.tandfonline.com\/doi\/pdf\/10.1080\/10556788.2024.2436173","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,30]],"date-time":"2025-05-30T13:28:33Z","timestamp":1748611713000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.tandfonline.com\/doi\/full\/10.1080\/10556788.2024.2436173"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,12,23]]},"references-count":44,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2025,5,4]]}},"alternative-id":["10.1080\/10556788.2024.2436173"],"URL":"https:\/\/doi.org\/10.1080\/10556788.2024.2436173","relation":{},"ISSN":["1055-6788","1029-4937"],"issn-type":[{"value":"1055-6788","type":"print"},{"value":"1029-4937","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,12,23]]},"assertion":[{"value":"The publishing and review policy for this title is described in its Aims & Scope.","order":1,"name":"peerreview_statement","label":"Peer Review Statement"},{"value":"http:\/\/www.tandfonline.com\/action\/journalInformation?show=aimsScope&journalCode=goms20","URL":"http:\/\/www.tandfonline.com\/action\/journalInformation?show=aimsScope&journalCode=goms20","order":2,"name":"aims_and_scope_url","label":"Aim & Scope"},{"value":"2023-08-31","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2024-11-12","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2024-12-23","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}