{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,14]],"date-time":"2026-06-14T16:59:15Z","timestamp":1781456355368,"version":"3.54.1"},"reference-count":45,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Mathematics and Computers in Simulation"],"published-print":{"date-parts":[[2026,11]]},"DOI":"10.1016\/j.matcom.2026.06.001","type":"journal-article","created":{"date-parts":[[2026,6,4]],"date-time":"2026-06-04T16:27:08Z","timestamp":1780590428000},"page":"510-532","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["A two-term inertial method for monotone VIPs: Implementation in multiclass classification and portfolio optimization"],"prefix":"10.1016","volume":"249","author":[{"given":"Zheng","family":"Jia","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jian-Wen","family":"Peng","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sani","family":"Salisu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yekini","family":"Shehu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"key":"10.1016\/j.matcom.2026.06.001_b1","series-title":"Applied Nonlinear Analysis","author":"Aubin","year":"1984"},{"key":"10.1016\/j.matcom.2026.06.001_b2","series-title":"Variational and Quasivariational Inequalities; Applications To Free Boundary Problems","author":"Baiocchi","year":"1984"},{"key":"10.1016\/j.matcom.2026.06.001_b3","first-page":"138","article-title":"Sul problema elastostatico di signorini con ambigue condizioni al contorno","volume":"34","author":"Fichera","year":"1963","journal-title":"Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Nat."},{"key":"10.1016\/j.matcom.2026.06.001_b4","series-title":"Numerical Analysis of Variational Inequalities","author":"Glowinski","year":"1981"},{"key":"10.1016\/j.matcom.2026.06.001_b5","doi-asserted-by":"crossref","first-page":"120","DOI":"10.1016\/0041-5553(87)90058-9","article-title":"Modification of the extragradient method for solving variational inequalities and certain optimization problems","volume":"27","author":"Khobotov","year":"1989","journal-title":"USSR Comput. Math. Math. Phys."},{"key":"10.1016\/j.matcom.2026.06.001_b6","series-title":"An Introduction To Variational Inequalities and their Applications","author":"Kinderlehrer","year":"1980"},{"key":"10.1016\/j.matcom.2026.06.001_b7","series-title":"Network Economics: A Variational Inequality Approach","author":"Nagurney","year":"1999"},{"key":"10.1016\/j.matcom.2026.06.001_b8","series-title":"Theory and Applications of Monotone Operators","first-page":"102","article-title":"\u201dVariational inequalities","author":"Stampacchia","year":"1968"},{"key":"10.1016\/j.matcom.2026.06.001_b9","first-page":"747","article-title":"The extragradient method for finding saddle points and other problems","volume":"12","author":"Korpelevich","year":"1976","journal-title":"\u00c8kon. I Mat. Metod."},{"key":"10.1016\/j.matcom.2026.06.001_b10","doi-asserted-by":"crossref","first-page":"845","DOI":"10.1007\/BF01141092","article-title":"A modification of the arrow-hurwicz method for finding saddle points","volume":"28","author":"Popov","year":"1980","journal-title":"Math. Notes"},{"key":"10.1016\/j.matcom.2026.06.001_b11","doi-asserted-by":"crossref","first-page":"1119","DOI":"10.1080\/02331934.2010.539689","article-title":"Extensions of korpelevich\u2019s extragradient method for the variational inequality problem in euclidean space","volume":"61","author":"Censor","year":"2011","journal-title":"Optimization"},{"key":"10.1016\/j.matcom.2026.06.001_b12","doi-asserted-by":"crossref","first-page":"318","DOI":"10.1007\/s10957-010-9757-3","article-title":"The subgradient extragradient method for solving variational inequalities in Hilbert space","volume":"148","author":"Censor","year":"2011","journal-title":"J. Optim. Theory Appl."},{"key":"10.1016\/j.matcom.2026.06.001_b13","doi-asserted-by":"crossref","first-page":"827","DOI":"10.1080\/10556788.2010.551536","article-title":"Strong convergence of subgradient extragradient methods for the variational inequality problem in Hilbert space","volume":"26","author":"Censor","year":"2011","journal-title":"Optim. Meth Softw."},{"key":"10.1016\/j.matcom.2026.06.001_b14","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1007\/s10559-014-9614-8","article-title":"An extragradient algorithm for monotone variational inequalities","volume":"50","author":"Malitsky","year":"2014","journal-title":"Cybernet. Systems Anal."},{"key":"10.1016\/j.matcom.2026.06.001_b15","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1007\/s10898-014-0150-x","article-title":"A hybrid method without extrapolation step for solving variational inequality problems","volume":"61","author":"Malitsky","year":"2015","journal-title":"J. Global Optim."},{"key":"10.1016\/j.matcom.2026.06.001_b16","doi-asserted-by":"crossref","first-page":"421","DOI":"10.1007\/s11081-020-09593-w","article-title":"A modified inertial subgradient extragradient method for solving variational inequalities","volume":"23","author":"Shehu","year":"2022","journal-title":"Optim. Eng."},{"key":"10.1016\/j.matcom.2026.06.001_b17","doi-asserted-by":"crossref","first-page":"1067","DOI":"10.1080\/00036811.2019.1634257","article-title":"Self-adaptive inertial subgradient extragradient algorithm for solving pseudomonotone variational inequalities","volume":"100","author":"Yang","year":"2021","journal-title":"Appl. Anal."},{"key":"10.1016\/j.matcom.2026.06.001_b18","doi-asserted-by":"crossref","first-page":"2247","DOI":"10.1080\/02331934.2018.1523404","article-title":"Modified subgradient extragradient algorithms for solving monotone variational inequalities","volume":"67","author":"Yang","year":"2018","journal-title":"Optimization"},{"key":"10.1016\/j.matcom.2026.06.001_b19","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1137\/S0363012998338806","article-title":"A modified forward\u2013backward splitting method for maximal monotone mappings","volume":"38","author":"Tseng","year":"2000","journal-title":"SIAM J. Control Optim."},{"key":"10.1016\/j.matcom.2026.06.001_b20","article-title":"An inertial subgradient extragradient algorithm with adaptive stepsizes for variational inequality problems","author":"Chang","year":"2021","journal-title":"Optim. Meth. Soft."},{"key":"10.1016\/j.matcom.2026.06.001_b21","doi-asserted-by":"crossref","first-page":"2199","DOI":"10.1080\/02331934.2019.1625355","article-title":"A subgradient extragradient algorithm with inertial effects for solving strongly pseudomonotone variational, inequalities","volume":"69","author":"Fan","year":"2020","journal-title":"Optimization"},{"key":"10.1016\/j.matcom.2026.06.001_b22","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1016\/j.apnum.2020.06.009","article-title":"Projection methods with alternating inertial steps for variational inequalities: Weak and linear convergence","volume":"157","author":"Shehu","year":"2020","journal-title":"Appl. Numer. Math."},{"key":"10.1016\/j.matcom.2026.06.001_b23","doi-asserted-by":"crossref","first-page":"80","DOI":"10.1016\/j.cam.2018.03.019","article-title":"Inertial extragradient algorithms for strongly pseudomonotone variational inequalities","volume":"341","author":"Thong","year":"2018","journal-title":"J. Comput. Appl. Math."},{"key":"10.1016\/j.matcom.2026.06.001_b24","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1007\/s11590-019-01511-z","article-title":"Self-adaptive inertial subgradient extragradient algorithms for solving pseudomonotone variational inequality problems","volume":"14","author":"Thong","year":"2020","journal-title":"Optim. Lett."},{"key":"10.1016\/j.matcom.2026.06.001_b25","doi-asserted-by":"crossref","first-page":"757","DOI":"10.1007\/s11590-020-01599-8","article-title":"An inertial popov\u2019s method for solving pseudomonotone variational inequalities","volume":"15","author":"Thong","year":"2021","journal-title":"Optim. Lett."},{"key":"10.1016\/j.matcom.2026.06.001_b26","first-page":"19 pp.","article-title":"Self-adaptive subgradient extragradient method with inertial modification for solving monotone variational inequality problems and quasi-nonexpansive fixed point problems","author":"Tian","year":"2019","journal-title":"J. Inequal. Appl."},{"key":"10.1016\/j.matcom.2026.06.001_b27","doi-asserted-by":"crossref","first-page":"502","DOI":"10.1137\/14097238X","article-title":"Projected reflected gradient methods for monotone variational inequalities","volume":"25","author":"Malitsky","year":"2015","journal-title":"SIAM J. Optim."},{"key":"10.1016\/j.matcom.2026.06.001_b28","first-page":"127","article-title":"Modified forward\u2013backward splitting method for variational inclusions","volume":"19","author":"Hieu","year":"2021"},{"issue":"3","key":"10.1016\/j.matcom.2026.06.001_b29","doi-asserted-by":"crossref","first-page":"720","DOI":"10.1016\/j.camwa.2016.05.028","article-title":"Numerical approach to monotone variational inequalities by a one-step projected reflected gradient method with line-search procedure","volume":"72","author":"Maing\u00e9","year":"2016","journal-title":"Comp. Math. Appl."},{"key":"10.1016\/j.matcom.2026.06.001_b30","doi-asserted-by":"crossref","first-page":"146","DOI":"10.1007\/s10957-016-0972-4","article-title":"Convergence of one-step projected gradient methods for variational inequalities","volume":"171","author":"Maing\u00e9","year":"2016","journal-title":"J. Optim. Theory Appl."},{"key":"10.1016\/j.matcom.2026.06.001_b31","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1007\/s10107-019-01416-w","article-title":"Golden ratio algorithms for variational inequalities","volume":"184","author":"Malitsky","year":"2020","journal-title":"Math. Program."},{"key":"10.1016\/j.matcom.2026.06.001_b32","doi-asserted-by":"crossref","first-page":"1451","DOI":"10.1137\/18M1207260","article-title":"A forward\u2013backward splitting method for monotone inclusions without cocoercivity","volume":"30","author":"Malitsky","year":"2020","journal-title":"SIAM J. Optim."},{"key":"10.1016\/j.matcom.2026.06.001_b33","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1007\/s10957-018-1351-0","article-title":"A modified projected gradient method for monotone variational inequalities","volume":"179","author":"Yang","year":"2018","journal-title":"J. Optim. Theory Appl."},{"key":"10.1016\/j.matcom.2026.06.001_b34","doi-asserted-by":"crossref","first-page":"168","DOI":"10.1007\/s40314-021-01540-4","article-title":"A general inertial projected gradient method for variational inequality problems","volume":"40","author":"Dong","year":"2021","journal-title":"Comp. Appl. Math."},{"key":"10.1016\/j.matcom.2026.06.001_b35","doi-asserted-by":"crossref","first-page":"408","DOI":"10.1016\/j.apnum.2021.09.013","article-title":"An explicit algorithm for solving monotone variational inequalities","volume":"171","author":"Thong","year":"2022","journal-title":"Appl. Numer. Math."},{"key":"10.1016\/j.matcom.2026.06.001_b36","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1007\/s10915-022-01989-3","article-title":"Inertial version of generalized projected reflected gradient method","volume":"93","author":"Iyiola","year":"2022","journal-title":"J. Sci. Comput."},{"key":"10.1016\/j.matcom.2026.06.001_b37","series-title":"CMS Books in Mathematics","article-title":"Convex analysis and monotone operator theory in hilbert spaces","author":"Bauschke","year":"2011"},{"key":"10.1016\/j.matcom.2026.06.001_b38","series-title":"Uniform Convexity, Hyperbolic Geometry, and Nonexpansive Mappings","author":"Goebel","year":"1984"},{"key":"10.1016\/j.matcom.2026.06.001_b39","series-title":"Nonlinear Functional Analysis","author":"Takahashi","year":"2000"},{"key":"10.1016\/j.matcom.2026.06.001_b40","doi-asserted-by":"crossref","first-page":"491","DOI":"10.1007\/s10589-020-00217-8","article-title":"Weak convergence of iterative methods for solving quasimonotone variational inequalities","volume":"77","author":"Liu","year":"2020","journal-title":"Comput. Optim. Appl."},{"key":"10.1016\/j.matcom.2026.06.001_b41","doi-asserted-by":"crossref","unstructured":"J. Duchi, S. Shalev-Shwartz, Y. Singer, T. Chandra, Efficient projections onto the \u21131-ball for learning in high dimensions, in: Proceedings of the 25th International Conference on Machine Learning (Pp. 272\u2013279), 2008, 2008.","DOI":"10.1145\/1390156.1390191"},{"key":"10.1016\/j.matcom.2026.06.001_b42","series-title":"Wine Quality","author":"Cortez","year":"2009"},{"issue":"4","key":"10.1016\/j.matcom.2026.06.001_b43","doi-asserted-by":"crossref","first-page":"547","DOI":"10.1016\/j.dss.2009.05.016","article-title":"Modeling wine preferences by data mining from physicochemical properties","volume":"47","author":"Cortez","year":"2009","journal-title":"Decis. Support Syst."},{"key":"10.1016\/j.matcom.2026.06.001_b44","series-title":"\u201dLetter Recognition","author":"Slate","year":"1991"},{"key":"10.1016\/j.matcom.2026.06.001_b45","series-title":"\u201dDataset for Sensorless Drive Diagnosis","author":"Bator","year":"2013"}],"container-title":["Mathematics and Computers in Simulation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0378475426002442?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0378475426002442?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,6,14]],"date-time":"2026-06-14T16:30:20Z","timestamp":1781454620000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0378475426002442"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,11]]},"references-count":45,"alternative-id":["S0378475426002442"],"URL":"https:\/\/doi.org\/10.1016\/j.matcom.2026.06.001","relation":{},"ISSN":["0378-4754"],"issn-type":[{"value":"0378-4754","type":"print"}],"subject":[],"published":{"date-parts":[[2026,11]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"A two-term inertial method for monotone VIPs: Implementation in multiclass classification and portfolio optimization","name":"articletitle","label":"Article Title"},{"value":"Mathematics and Computers in Simulation","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.matcom.2026.06.001","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}]}}