{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,25]],"date-time":"2026-04-25T14:57:27Z","timestamp":1777129047975,"version":"3.51.4"},"reference-count":24,"publisher":"World Scientific Pub Co Pte Ltd","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Asia Pac. J. Oper. Res."],"published-print":{"date-parts":[[2022,4]]},"abstract":"<jats:p> In this paper, we propose a self-adaptive inertial projection and contraction algorithm, by combining backtracking search with the inertial projection and contraction algorithm, for solving monotone variational inequality in Hilbert space. This algorithm not only circumvents the restrictive assumption of Lipschitz continuity of the operator, but also gives more suitable and feasible parameters. Under the assumption that the operator is continuous and monotone, we establish weak convergence for proposed algorithm. Finally, we report some preliminary computational results to show the efficiency and advantage of the algorithm. <\/jats:p>","DOI":"10.1142\/s0217595921500214","type":"journal-article","created":{"date-parts":[[2021,5,18]],"date-time":"2021-05-18T02:05:11Z","timestamp":1621303511000},"source":"Crossref","is-referenced-by-count":3,"title":["Self-Adaptive Inertial Projection and Contraction Algorithm for Monotone Variational Inequality"],"prefix":"10.1142","volume":"39","author":[{"given":"Xue","family":"Gao","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Jiangsu Key Lab for NSLSCS, Nanjing Normal University, Nanjing 210023, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xingju","family":"Cai","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Jiangsu Key Lab for NSLSCS, Nanjing Normal University, Nanjing 210023, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xueye","family":"Wang","sequence":"additional","affiliation":[{"name":"Qishuyan Senior High School of Changzhou, Changzhou 213011, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2021,6,8]]},"reference":[{"key":"S0217595921500214BIB001","first-page":"103","volume":"13","author":"Alfredo NI","year":"1994","journal-title":"Computational and Applied Mathematics"},{"key":"S0217595921500214BIB002","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623403427859"},{"key":"S0217595921500214BIB003","doi-asserted-by":"publisher","DOI":"10.1023\/A:1011253113155"},{"key":"S0217595921500214BIB004","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-016-0992-8"},{"key":"S0217595921500214BIB005","doi-asserted-by":"publisher","DOI":"10.1137\/130910294"},{"key":"S0217595921500214BIB006","doi-asserted-by":"publisher","DOI":"10.1287\/moor.2016.0817"},{"key":"S0217595921500214BIB007","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4419-9467-7"},{"key":"S0217595921500214BIB008","volume-title":"Parallel and Distributed Computation\u200a Numerical Methods","author":"Bertsekas DP","year":"1989"},{"key":"S0217595921500214BIB009","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2015.01.017"},{"key":"S0217595921500214BIB010","doi-asserted-by":"publisher","DOI":"10.1007\/s10589-013-9599-7"},{"key":"S0217595921500214BIB011","doi-asserted-by":"publisher","DOI":"10.1080\/10556788.2010.551536"},{"key":"S0217595921500214BIB012","doi-asserted-by":"publisher","DOI":"10.1007\/s10957-010-9757-3"},{"key":"S0217595921500214BIB013","volume-title":"Numerical Methods for Unconstrained Optimization and Nonlinear Equations","author":"Dennis JE","year":"1997"},{"key":"S0217595921500214BIB014","doi-asserted-by":"publisher","DOI":"10.1007\/s10898-017-0506-0"},{"key":"S0217595921500214BIB015","doi-asserted-by":"publisher","DOI":"10.1080\/02331934.2016.1239266"},{"key":"S0217595921500214BIB016","doi-asserted-by":"publisher","DOI":"10.1007\/s00245-001-0029-3"},{"key":"S0217595921500214BIB017","first-page":"54","volume":"14","author":"He BS","year":"1996","journal-title":"Journal of Computational Mathematics"},{"key":"S0217595921500214BIB018","doi-asserted-by":"publisher","DOI":"10.1007\/s002459900037"},{"key":"S0217595921500214BIB019","doi-asserted-by":"publisher","DOI":"10.1023\/A:1013096613105"},{"key":"S0217595921500214BIB020","first-page":"747","volume":"12","author":"Korpelevich GM","year":"1976","journal-title":"Matecon"},{"key":"S0217595921500214BIB021","doi-asserted-by":"publisher","DOI":"10.1007\/s10851-015-0565-0"},{"key":"S0217595921500214BIB022","doi-asserted-by":"publisher","DOI":"10.1137\/130942954"},{"key":"S0217595921500214BIB023","doi-asserted-by":"publisher","DOI":"10.1016\/0041-5553(64)90137-5"},{"key":"S0217595921500214BIB024","doi-asserted-by":"publisher","DOI":"10.7153\/mia-07-45"}],"container-title":["Asia-Pacific Journal of Operational Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0217595921500214","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,4,28]],"date-time":"2022-04-28T08:53:05Z","timestamp":1651135985000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S0217595921500214"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,6,8]]},"references-count":24,"journal-issue":{"issue":"02","published-print":{"date-parts":[[2022,4]]}},"alternative-id":["10.1142\/S0217595921500214"],"URL":"https:\/\/doi.org\/10.1142\/s0217595921500214","relation":{},"ISSN":["0217-5959","1793-7019"],"issn-type":[{"value":"0217-5959","type":"print"},{"value":"1793-7019","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,6,8]]},"article-number":"2150021"}}