{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:24:59Z","timestamp":1753881899851,"version":"3.41.2"},"reference-count":33,"publisher":"World Scientific Pub Co Pte Ltd","issue":"05","funder":[{"DOI":"10.13039\/501100012166","name":"National Key R&D Program of China","doi-asserted-by":"crossref","award":["2018YFB0505000"],"award-info":[{"award-number":["2018YFB0505000"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"crossref"}]},{"name":"National Key AI Program of China","award":["2018AAA0100500"],"award-info":[{"award-number":["2018AAA0100500"]}]},{"name":"Natural Science Foudation of Guangdong","award":["2018A030307064"],"award-info":[{"award-number":["2018A030307064"]}]},{"name":"Teaching Quality Engineering Construction Project of Jiaying University in 2022","award":["JYJG2022239"],"award-info":[{"award-number":["JYJG2022239"]}]},{"name":"Teaching Quality Engineering Construction Project of Jiaying University in 2022","award":["ZLGC2022703"],"award-info":[{"award-number":["ZLGC2022703"]}]},{"name":"Teaching Quality Engineering Construction Project of Jiaying University in 2022","award":["JYJG2022110"],"award-info":[{"award-number":["JYJG2022110"]}]},{"name":"Guangdong Provincial Teaching Quality Engineering Project in 2022"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Wavelets Multiresolut Inf. Process."],"published-print":{"date-parts":[[2023,9]]},"abstract":"<jats:p>Tremendous efficient optimization methods have been proposed for strongly convex objectives optimization in modern machine learning. For non-strongly convex objectives, a popular approach is to apply a reduction from non-strongly convex to a strongly convex case via regularization techniques. Reduction on objectives with adaptive decrease on regularization tightens the optimal convergence of algorithms to be independent on logarithm factor. However, the initialization of parameter of regularization has a great impact on the performance of the reduction. In this paper, we propose an aggressive reduction to reduce the complexity of optimization for non-strongly convex objectives, and our reduction eliminates the impact of the initialization of parameter on the convergent performances of algorithms. Aggressive reduction not only adaptively decreases the regularization parameter, but also modifies regularization term as the distance between current point and the approximate minimizer. Our aggressive reduction can also shave off the non-optimal logarithm term theoretically, and make the convergent performance of algorithm more compact practically. Experimental results on logistic regression and image deblurring confirm this success in practice.<\/jats:p>","DOI":"10.1142\/s0219691323500170","type":"journal-article","created":{"date-parts":[[2023,5,22]],"date-time":"2023-05-22T06:46:06Z","timestamp":1684737966000},"source":"Crossref","is-referenced-by-count":0,"title":["An aggressive reduction on the complexity of optimization for non-strongly convex objectives"],"prefix":"10.1142","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8670-5786","authenticated-orcid":false,"given":"Zhijian","family":"Luo","sequence":"first","affiliation":[{"name":"School of Computer, Jiaying University, Meizhou, 514015, P. R. China"}]},{"given":"Siyu","family":"Chen","sequence":"additional","affiliation":[{"name":"College of Computer Science and Technology, Zhejiang University, Hangzhou, 310027, P. R. China"}]},{"given":"Yueen","family":"Hou","sequence":"additional","affiliation":[{"name":"School of Computer, Jiaying University, Meizhou, 514015, P. R. China"}]},{"given":"Yanzeng","family":"Gao","sequence":"additional","affiliation":[{"name":"School of Computer, Jiaying University, Meizhou, 514015, P. R. China"}]},{"given":"Yuntao","family":"Qian","sequence":"additional","affiliation":[{"name":"College of Computer Science and Technology, Zhejiang University, Hangzhou, 310027, P. R. China"}]}],"member":"219","published-online":{"date-parts":[[2023,5,20]]},"reference":[{"issue":"1","key":"S0219691323500170BIB001","first-page":"8194","volume":"18","author":"Allen-Zhu Z.","year":"2017","journal-title":"J. Mach. Learn. Res."},{"key":"S0219691323500170BIB002","first-page":"1614","volume":"29","author":"Allen-Zhu Z.","year":"2016","journal-title":"Proc. Neural Inf. Process. Syst."},{"key":"S0219691323500170BIB003","first-page":"1080","volume-title":"Pro. Int. Conf. Mach. Learn.","volume":"48","author":"Allen-Zhu Z.","year":"2016"},{"key":"S0219691323500170BIB005","first-page":"27:1","volume":"2","author":"Chang C.-C.","year":"2011","journal-title":"ACM Trans. Intell. Syst. Tech."},{"key":"S0219691323500170BIB006","first-page":"676","volume":"29","author":"Defazio A.","year":"2016","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"S0219691323500170BIB007","first-page":"1646","volume":"2","author":"Defazio A.","year":"2014","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"S0219691323500170BIB008","first-page":"1125","volume-title":"International Conference on Machine Learning","author":"Defazio A.","year":"2014"},{"key":"S0219691323500170BIB009","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10107-020-01566-2","volume":"191","author":"Driggs D.","year":"2022","journal-title":"Math. Program."},{"issue":"11","key":"S0219691323500170BIB010","doi-asserted-by":"crossref","first-page":"1968","DOI":"10.1109\/JPROC.2020.3028013","volume":"108","author":"Gower R. M.","year":"2020","journal-title":"Proc. IEEE"},{"issue":"2","key":"S0219691323500170BIB011","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1007\/s11075-007-9136-9","volume":"46","author":"Hansen P. C.","year":"2007","journal-title":"Numer. Algor."},{"key":"S0219691323500170BIB012","doi-asserted-by":"crossref","first-page":"541","DOI":"10.1007\/s10957-018-01469-5","volume":"181","author":"Hien L. T. K.","year":"2019","journal-title":"J. Optim. Theory Appl."},{"key":"S0219691323500170BIB013","first-page":"315","volume":"26","author":"Johnson R.","year":"2013","journal-title":"Adv. Neural Inf. Process. Syst."},{"volume-title":"Logistic Regression","year":"2002","author":"Kleinbaum D. G.","key":"S0219691323500170BIB014"},{"issue":"2","key":"S0219691323500170BIB015","doi-asserted-by":"crossref","first-page":"242","DOI":"10.1109\/JSTSP.2015.2505682","volume":"10","author":"Kone\u010dn\u1ef3 J.","year":"2016","journal-title":"IEEE J. Sel. Topics Signal Process."},{"key":"S0219691323500170BIB016","doi-asserted-by":"crossref","first-page":"9","DOI":"10.3389\/fams.2017.00009","volume":"3","author":"Kone\u010dn\u1ef3 J.","year":"2017","journal-title":"Front. Appl. Math. Statist."},{"issue":"7553","key":"S0219691323500170BIB017","doi-asserted-by":"crossref","first-page":"436","DOI":"10.1038\/nature14539","volume":"521","author":"LeCun Y.","year":"2015","journal-title":"Nature"},{"key":"S0219691323500170BIB019","first-page":"3384","volume":"28","author":"Lin H.","year":"2015","journal-title":"Adv. Neural Inf. Process. Syst."},{"issue":"4","key":"S0219691323500170BIB020","doi-asserted-by":"crossref","first-page":"2244","DOI":"10.1137\/141000270","volume":"25","author":"Lin Q.","year":"2015","journal-title":"SIAM J. Optim."},{"key":"S0219691323500170BIB021","doi-asserted-by":"crossref","first-page":"166551","DOI":"10.1109\/ACCESS.2019.2953288","volume":"7","author":"Luo Z.","year":"2019","journal-title":"IEEE Access"},{"issue":"2","key":"S0219691323500170BIB022","doi-asserted-by":"crossref","first-page":"829","DOI":"10.1137\/140957639","volume":"25","author":"Mairal J.","year":"2015","journal-title":"SIAM J. Optim."},{"key":"S0219691323500170BIB023","first-page":"608","volume":"30","author":"Murata T.","year":"2017","journal-title":"Adv. Neural Inf. Process. Syst."},{"volume-title":"Introductory Lectures on Convex Optimization: A Basic Course","year":"2013","author":"Nesterov Y.","key":"S0219691323500170BIB024"},{"key":"S0219691323500170BIB025","first-page":"2613","volume-title":"International Conference on Machine Learning","author":"Nguyen L. M.","year":"2017"},{"key":"S0219691323500170BIB026","volume":"27","author":"Nitanda A.","year":"2014","journal-title":"Adv. Neural Inf. Process. Syst."},{"issue":"12","key":"S0219691323500170BIB027","doi-asserted-by":"crossref","first-page":"1565","DOI":"10.1038\/nbt1206-1565","volume":"24","author":"Noble W. S.","year":"2006","journal-title":"Nat. Biotechnol."},{"issue":"2","key":"S0219691323500170BIB028","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1080\/10618600.2000.10474883","volume":"9","author":"Osborne M. R.","year":"2000","journal-title":"J. Comput. Graph. Stat."},{"key":"S0219691323500170BIB029","first-page":"2332","volume-title":"Proceedings of the International Conference on Machine Learning","author":"Sa C. D.","year":"2015"},{"key":"S0219691323500170BIB030","first-page":"819","volume-title":"Artificial Intelligence and Statistics","author":"Schmidt M.","year":"2015"},{"issue":"1","key":"S0219691323500170BIB031","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1007\/s10107-016-1030-6","volume":"162","author":"Schmidt M. W.","year":"2017","journal-title":"Math. Program."},{"issue":"4","key":"S0219691323500170BIB033","doi-asserted-by":"crossref","first-page":"2057","DOI":"10.1137\/140961791","volume":"24","author":"Xiao L.","year":"2014","journal-title":"SIAM J. Optim."},{"key":"S0219691323500170BIB034","first-page":"353","volume-title":"Proceedings of the International Conference on Machine Learning","author":"Zhang Y.","year":"2015"},{"key":"S0219691323500170BIB035","first-page":"5980","volume-title":"Proceedings of the International Conference on Machine Learning","author":"Zhou K.","year":"2018"},{"issue":"476","key":"S0219691323500170BIB036","doi-asserted-by":"crossref","first-page":"1418","DOI":"10.1198\/016214506000000735","volume":"101","author":"Zou H.","year":"2006","journal-title":"J. Am. Stat. Assoc."}],"container-title":["International Journal of Wavelets, Multiresolution and Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219691323500170","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,10,20]],"date-time":"2024-10-20T20:56:17Z","timestamp":1729457777000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S0219691323500170"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,5,20]]},"references-count":33,"journal-issue":{"issue":"05","published-print":{"date-parts":[[2023,9]]}},"alternative-id":["10.1142\/S0219691323500170"],"URL":"https:\/\/doi.org\/10.1142\/s0219691323500170","relation":{},"ISSN":["0219-6913","1793-690X"],"issn-type":[{"type":"print","value":"0219-6913"},{"type":"electronic","value":"1793-690X"}],"subject":[],"published":{"date-parts":[[2023,5,20]]},"article-number":"2350017"}}