{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:06:21Z","timestamp":1753884381344,"version":"3.41.2"},"reference-count":19,"publisher":"World Scientific Pub Co Pte Ltd","issue":"04","funder":[{"DOI":"10.13039\/501100001809","name":"National Science Foundation of China","doi-asserted-by":"crossref","award":["11771003","52075006","1217011635"],"award-info":[{"award-number":["11771003","52075006","1217011635"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100004761","name":"Natural Science Foundation of Hunan Province of China","doi-asserted-by":"crossref","award":["2021JJ30167","2022JJ30675"],"award-info":[{"award-number":["2021JJ30167","2022JJ30675"]}],"id":[{"id":"10.13039\/501100004761","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Hunan Provincial Education Department of China","award":["21B0807"],"award-info":[{"award-number":["21B0807"]}]},{"DOI":"10.13039\/501100018579","name":"Training Program for Excellent Young Innovators of Changsha","doi-asserted-by":"crossref","award":["kq2209021"],"award-info":[{"award-number":["kq2209021"]}],"id":[{"id":"10.13039\/501100018579","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Asia Pac. J. Oper. Res."],"published-print":{"date-parts":[[2023,8]]},"abstract":"<jats:p> In machine learning, most models can be transformed into unconstrained optimization problems, so how to solve the unconstrained optimization problem for different objective functions is always a hot issue. In this paper, a class of unconstrained optimization where objection function has [Formula: see text]th-order derivative and Lipschitz continuous simultaneously is studied. To handle such problems, we propose an accelerated regularized Chebyshev\u2013Halley method based on the Accelerated Hybrid Proximal Extragradient (A-HPE) framework. It proves that convergence complexity of the proposed method is [Formula: see text], which is consistent with the lower iteration complexity bound for third-order tensor methods. Numerical experiments on functions in machine learning demonstrate the promising performance of the proposed method. <\/jats:p>","DOI":"10.1142\/s0217595923400080","type":"journal-article","created":{"date-parts":[[2023,1,19]],"date-time":"2023-01-19T06:35:27Z","timestamp":1674110127000},"source":"Crossref","is-referenced-by-count":1,"title":["An Accelerated Regularized Chebyshev\u2013Halley Method for Unconstrained Optimization"],"prefix":"10.1142","volume":"40","author":[{"given":"Jianyu","family":"Xiao","sequence":"first","affiliation":[{"name":"Beijing Institute for Scientific and Engineering Computing, Faculty of Science, Beijing University of Technology, 100 Pingleyuan, Chaoyang District, Beijing 100124, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haibin","family":"Zhang","sequence":"additional","affiliation":[{"name":"Beijing Institute for Scientific and Engineering Computing, Faculty of Science, Beijing University of Technology, 100 Pingleyuan, Chaoyang District, Beijing 100124, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Huan","family":"Gao","sequence":"additional","affiliation":[{"name":"College of Mathematics and Computational Science, Hunan First Normal University, 1015 Fenglin 3rd Road, Yuelu District, Changsha, Hunan 410205, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2023,5,27]]},"reference":[{"key":"S0217595923400080BIB001","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1007\/s10107-018-1293-1","volume":"178","author":"Arjevani Y","year":"2019","journal-title":"Mathematical Programming"},{"key":"S0217595923400080BIB002","volume-title":"Estimate Sequence Methods: Extensions and Approximations","volume":"2","author":"Baes M","year":"2009"},{"key":"S0217595923400080BIB003","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1080\/10556788.2011.602076","volume":"27","author":"Cartis C","year":"2012","journal-title":"Optimization Methods and Software"},{"issue":"2","key":"S0217595923400080BIB004","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s40314-022-01774-w","volume":"41","author":"Danmalam KU","year":"2022","journal-title":"Computational and Applied Mathematics"},{"key":"S0217595923400080BIB005","first-page":"1374","volume-title":"Conf. Learning Theory","author":"Gasnikov A","year":"2019"},{"key":"S0217595923400080BIB006","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1137\/17M1142077","volume":"29","author":"Grapiglia GN","year":"2019","journal-title":"SIAM Journal on Optimization"},{"issue":"4","key":"S0217595923400080BIB008","doi-asserted-by":"crossref","first-page":"533","DOI":"10.1007\/BF00933151","volume":"26","author":"Hoffmann KH","year":"1978","journal-title":"Journal of Optimization Theory and Applications"},{"issue":"2","key":"S0217595923400080BIB009","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1007\/s10107-007-0196-3","volume":"118","author":"Ito K","year":"2009","journal-title":"Mathematical Programming"},{"key":"S0217595923400080BIB010","doi-asserted-by":"crossref","first-page":"2897","DOI":"10.1137\/19M1286025","volume":"30","author":"Jiang B","year":"2020","journal-title":"SIAM Journal on Optimization"},{"issue":"4","key":"S0217595923400080BIB011","doi-asserted-by":"crossref","first-page":"2057","DOI":"10.1137\/140961791","volume":"24","author":"Lin X","year":"2014","journal-title":"SIAM Journal on Optimization"},{"key":"S0217595923400080BIB012","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1016\/j.neucom.2020.07.070","volume":"419","author":"Liu Y","year":"2021","journal-title":"Neurocomputing"},{"issue":"6","key":"S0217595923400080BIB013","doi-asserted-by":"crossref","first-page":"2021","DOI":"10.1080\/10556788.2021.2022148","volume":"37","author":"Marques Alves M","year":"2022","journal-title":"Optimization Methods and Software"},{"key":"S0217595923400080BIB014","doi-asserted-by":"crossref","first-page":"1092","DOI":"10.1137\/110833786","volume":"23","author":"Monteiro RDC","year":"2013","journal-title":"SIAM Journal on Optimization"},{"issue":"1","key":"S0217595923400080BIB015","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1007\/s10107-006-0089-x","volume":"112","author":"Nesterov Y","year":"2008","journal-title":"Mathematical Programming"},{"key":"S0217595923400080BIB016","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1007\/s10107-019-01449-1","volume":"186","author":"Nesterov Y","year":"2018","journal-title":"Mathematical Programming"},{"issue":"1","key":"S0217595923400080BIB017","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1007\/s10107-006-0706-8","volume":"108","author":"Nesterov Y","year":"2006","journal-title":"Mathematical Programming"},{"key":"S0217595923400080BIB018","first-page":"32","volume-title":"Advances in Neural Information Processing Systems","author":"Salehi F","year":"2019"},{"key":"S0217595923400080BIB019","doi-asserted-by":"crossref","first-page":"1797","DOI":"10.1137\/19M1290243","volume":"31","author":"Song C","year":"2021","journal-title":"SIAM Journal on Optimization"},{"key":"S0217595923400080BIB020","first-page":"1","volume-title":"IEEE\/ACIS th Int. Conf. Computer and Information Science (ICIS)","author":"Wu JY","year":"2016"}],"container-title":["Asia-Pacific Journal of Operational Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0217595923400080","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,31]],"date-time":"2023-08-31T07:02:28Z","timestamp":1693465348000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S0217595923400080"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,5,27]]},"references-count":19,"journal-issue":{"issue":"04","published-print":{"date-parts":[[2023,8]]}},"alternative-id":["10.1142\/S0217595923400080"],"URL":"https:\/\/doi.org\/10.1142\/s0217595923400080","relation":{},"ISSN":["0217-5959","1793-7019"],"issn-type":[{"type":"print","value":"0217-5959"},{"type":"electronic","value":"1793-7019"}],"subject":[],"published":{"date-parts":[[2023,5,27]]},"article-number":"2340008"}}