{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:32:51Z","timestamp":1753882371822,"version":"3.41.2"},"reference-count":24,"publisher":"World Scientific Pub Co Pte Ltd","issue":"03","funder":[{"DOI":"10.13039\/501100003787","name":"Natural Science Foundation of Hebei Province","doi-asserted-by":"crossref","award":["A2022201002"],"award-info":[{"award-number":["A2022201002"]}],"id":[{"id":"10.13039\/501100003787","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Asia Pac. J. Oper. Res."],"published-print":{"date-parts":[[2025,6]]},"abstract":"<jats:p> Semi-infinite minimax problems are widely utilized in various fields; however, there is a scarcity of algorithms that can directly tackle convex-convex and convex-concave semi-infinite minimax problems. An inexact algorithm based on the bundle method is introduced in this paper, which can be directly applied to solve both types of semi-infinite minimax problems. The novel algorithm offers the advantage of not requiring exact solutions for the inner maximization problem but only necessitates optimal solution with a certain level of precision. Additionally, the augmentation function method is employed to address nonconvergence issues encountered in traditional bundle method when dealing with convex-convex minimax problems. Global convergence of our algorithm is proven under reasonable assumptions. Numerical results from several examples demonstrate the effectiveness and practicality of our proposed approach. <\/jats:p>","DOI":"10.1142\/s0217595924500192","type":"journal-article","created":{"date-parts":[[2024,7,12]],"date-time":"2024-07-12T14:56:35Z","timestamp":1720796195000},"source":"Crossref","is-referenced-by-count":0,"title":["An Inexact Bundle Method for Semi-Infinite Minimax Problems"],"prefix":"10.1142","volume":"42","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4131-6955","authenticated-orcid":false,"given":"Tianyou","family":"Shang","sequence":"first","affiliation":[{"name":"Hebei Key Laboratory of Machine, Learning and Computational Intelligence, College of Mathematics and Information Science, Hebei University, Baoding 071002, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8735-1422","authenticated-orcid":false,"given":"Ke","family":"Su","sequence":"additional","affiliation":[{"name":"Hebei Key Laboratory of Machine, Learning and Computational Intelligence, College of Mathematics and Information Science, Hebei University, Baoding 071002, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7479-6396","authenticated-orcid":false,"given":"Yanshu","family":"Wei","sequence":"additional","affiliation":[{"name":"Hebei Key Laboratory of Machine, Learning and Computational Intelligence, College of Mathematics and Information Science, Hebei University, Baoding 071002, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6193-7639","authenticated-orcid":false,"given":"Bing","family":"Zhao","sequence":"additional","affiliation":[{"name":"Hebei Key Laboratory of Machine, Learning and Computational Intelligence, College of Mathematics and Information Science, Hebei University, Baoding 071002, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2024,8,7]]},"reference":[{"key":"S0217595924500192BIB001","doi-asserted-by":"publisher","DOI":"10.1137\/080734510"},{"key":"S0217595924500192BIB002","doi-asserted-by":"publisher","DOI":"10.1007\/BF01204183"},{"volume-title":"Nonsmooth Analysis and Control Theory","year":"2001","author":"Clarke FH","key":"S0217595924500192BIB003"},{"key":"S0217595924500192BIB004","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623402411459"},{"key":"S0217595924500192BIB005","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2014.07.033"},{"key":"S0217595924500192BIB006","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-3403-4"},{"key":"S0217595924500192BIB007","doi-asserted-by":"publisher","DOI":"10.1007\/s10589-015-9762-4"},{"key":"S0217595924500192BIB008","doi-asserted-by":"publisher","DOI":"10.1137\/1035089"},{"key":"S0217595924500192BIB009","doi-asserted-by":"publisher","DOI":"10.1007\/s11075-021-01128-3"},{"key":"S0217595924500192BIB010","doi-asserted-by":"publisher","DOI":"10.1142\/S0217595921400157"},{"volume-title":"Numerical Optimization","year":"2006","author":"Jorge Nocedal SJW","key":"S0217595924500192BIB011"},{"key":"S0217595924500192BIB012","doi-asserted-by":"publisher","DOI":"10.1287\/ijoc.2021.1122"},{"key":"S0217595924500192BIB013","doi-asserted-by":"publisher","DOI":"10.1023\/A:1005240024644"},{"key":"S0217595924500192BIB014","doi-asserted-by":"publisher","DOI":"10.1007\/s10898-017-0565-2"},{"key":"S0217595924500192BIB015","doi-asserted-by":"publisher","DOI":"10.1007\/s10589-015-9810-0"},{"key":"S0217595924500192BIB016","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.1976.1101196"},{"key":"S0217595924500192BIB017","doi-asserted-by":"publisher","DOI":"10.1109\/PROC.1984.13086"},{"key":"S0217595924500192BIB018","doi-asserted-by":"publisher","DOI":"10.1080\/03052157608960598"},{"key":"S0217595924500192BIB019","doi-asserted-by":"publisher","DOI":"10.1007\/s10957-021-01938-4"},{"key":"S0217595924500192BIB020","doi-asserted-by":"publisher","DOI":"10.1080\/02331934.2020.1763990"},{"key":"S0217595924500192BIB021","doi-asserted-by":"publisher","DOI":"10.1142\/S0217595921500159"},{"key":"S0217595924500192BIB022","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2022.114949"},{"volume-title":"Nonsmooth Analysis","year":"2007","author":"Winfried S","key":"S0217595924500192BIB023"},{"key":"S0217595924500192BIB024","doi-asserted-by":"publisher","DOI":"10.1023\/B:ANOR.0000004764.76984.30"}],"container-title":["Asia-Pacific Journal of Operational Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0217595924500192","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,13]],"date-time":"2025-06-13T07:47:41Z","timestamp":1749800861000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S0217595924500192"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,8,7]]},"references-count":24,"journal-issue":{"issue":"03","published-print":{"date-parts":[[2025,6]]}},"alternative-id":["10.1142\/S0217595924500192"],"URL":"https:\/\/doi.org\/10.1142\/s0217595924500192","relation":{},"ISSN":["0217-5959","1793-7019"],"issn-type":[{"type":"print","value":"0217-5959"},{"type":"electronic","value":"1793-7019"}],"subject":[],"published":{"date-parts":[[2024,8,7]]},"article-number":"2450019"}}