{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T21:42:28Z","timestamp":1648590148984},"reference-count":34,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2021,8,6]],"date-time":"2021-08-06T00:00:00Z","timestamp":1628208000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,8,6]],"date-time":"2021-08-06T00:00:00Z","timestamp":1628208000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/100014718","name":"Innovative Research Group Project of the National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11701050"],"award-info":[{"award-number":["11701050"]}],"id":[{"id":"10.13039\/100014718","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11771003"],"award-info":[{"award-number":["11771003"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2022,4]]},"DOI":"10.1007\/s11075-021-01172-z","type":"journal-article","created":{"date-parts":[[2021,8,6]],"date-time":"2021-08-06T07:03:15Z","timestamp":1628233395000},"page":"1769-1798","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Inertial-type incremental constraint projection method for solving variational inequalities without Lipschitz continuity"],"prefix":"10.1007","volume":"89","author":[{"given":"W. Y.","family":"Wang","sequence":"first","affiliation":[]},{"given":"F. Q.","family":"Xia","sequence":"additional","affiliation":[]},{"given":"K.","family":"Tu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,8,6]]},"reference":[{"key":"1172_CR1","doi-asserted-by":"publisher","first-page":"278","DOI":"10.1006\/jdeq.2001.4034","volume":"179","author":"H Attouch","year":"2002","unstructured":"Attouch, H., Czarnecki, M.O.: Asymptotic control and stabilization of nonlinear oscillators with nonisolated equilibria. J. Differential Equations. 179, 278\u2013310 (2002)","journal-title":"J. Differential Equations."},{"key":"1172_CR2","volume-title":"Optimization Methodes Num\u00e9riques","author":"A Auslender","year":"1976","unstructured":"Auslender, A.: Optimization Methodes Num\u00e9riques. Masson, Paris (1976)"},{"key":"1172_CR3","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1142\/S0219199700000025","volume":"2","author":"H Attouch","year":"2000","unstructured":"Attouch, H., Goudon, X., Redont, P.: The heavy ball with friction I. The continuous dynamical system. Commun. Contemp. Math. 2, 1\u201334 (2000)","journal-title":"Commun. Contemp. Math."},{"key":"1172_CR4","first-page":"15","volume":"1705\u20131710","author":"AB Bakusinskii","year":"1974","unstructured":"Bakusinskii, A.B., Polyak, B.T.: On the solution of variational inequalities. Sov. Math. Dokl. 1705\u20131710, 15 (1974)","journal-title":"Sov. Math. Dokl."},{"key":"1172_CR5","first-page":"81","volume":"890\u2013893","author":"RE Bruck","year":"1975","unstructured":"Bruck, R.E.: An iterative solution of a variational inequality for certain monotone operators in Hilbert space. Bull. Amer. Math. Soc. 890\u2013893, 81 (1975)","journal-title":"Bull. Amer. Math. Soc."},{"key":"1172_CR6","doi-asserted-by":"publisher","first-page":"247","DOI":"10.1007\/s10589-009-9246-5","volume":"46","author":"JY Bello Cruz","year":"2010","unstructured":"Bello Cruz, J.Y., Iusem, A.N.: Convergence of direct methods for paramonotone variational inequalities. Comput. Optim. Appl. 46, 247\u2013263 (2010)","journal-title":"Comput. Optim. Appl."},{"key":"1172_CR7","doi-asserted-by":"publisher","first-page":"855","DOI":"10.1080\/02331934.2010.536232","volume":"61","author":"JY Bello Cruz","year":"2012","unstructured":"Bello Cruz, J.Y., Iusem, A.N.: An explicit algorithm for monotone variational inequalities. Optimization. 61, 855\u2013871 (2012)","journal-title":"Optimization."},{"key":"1172_CR8","volume-title":"Dynamic programming and optimal control, Vol. II: Approximate Dynamic Programming","author":"DP Bertsekas","year":"2012","unstructured":"Bertsekas, D.P.: Dynamic programming and optimal control, Vol. II: Approximate Dynamic Programming. Athena Scientific, Belmont (2012)"},{"issue":"2","key":"1172_CR9","doi-asserted-by":"publisher","first-page":"318","DOI":"10.1007\/s10957-010-9757-3","volume":"148","author":"Y Censor","year":"2011","unstructured":"Censor, Y., Gibali, A., Reich, S.: The subgradient extragradient method for solving variational inequalities in Hilbert space. J.Optim. Theory Appl. 148(2), 318\u2013335 (2011)","journal-title":"J.Optim. Theory Appl."},{"key":"1172_CR10","doi-asserted-by":"publisher","first-page":"521","DOI":"10.1007\/PL00011384","volume":"88","author":"JP Crouzeix","year":"2000","unstructured":"Crouzeix, J.P., Marcotte, P., Zhu, D.L.: Conditions ensuring the applicability of cutting-plane methods for solving variational inequalities. Math. Program. 88, 521\u2013539 (2000)","journal-title":"Math. Program."},{"key":"1172_CR11","first-page":"12","volume":"195-225","author":"C Charalambous","year":"1977","unstructured":"Charalambous, C.: Nonlinear least pth optimization and nonlinear programming. Math. Program. 195-225, 12 (1977)","journal-title":"Math. Program."},{"key":"1172_CR12","first-page":"21","volume":"20","author":"VT Duong","year":"2019","unstructured":"Duong, V.T., Gibali, A.: Extragradient methods for solving non-Lipschitzian pseudo-monotone variational inequalities. J. Fixed Point Theory Appl. 20, 21 (2019)","journal-title":"J. Fixed Point Theory Appl."},{"key":"1172_CR13","doi-asserted-by":"publisher","first-page":"927","DOI":"10.1007\/s11075-017-0467-x","volume":"79","author":"QL Dong","year":"2018","unstructured":"Dong, Q.L., Jiang, D., Gibali, A.: A modified subgradient extragradient method for solving the variational inequality problem. Numer. Algorithms. 79, 927\u2013940 (2018)","journal-title":"Numer. Algorithms."},{"key":"1172_CR14","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1016\/0377-0427(84)90051-7","volume":"10","author":"M Fukushima","year":"1984","unstructured":"Fukushima, M.: On the convergence of a class of outer approximation algorithms for convex programs. J. Comput. Appl. Math. 10, 147\u2013156 (1984)","journal-title":"J. Comput. Appl. Math."},{"key":"1172_CR15","first-page":"70","volume":"709-711","author":"AA Goldstein","year":"1964","unstructured":"Goldstein, A.A.: Convex programming in Hilbert space. Bull. Amer. Math. Soc. 709-711, 70 (1964)","journal-title":"Bull. Amer. Math. Soc."},{"key":"1172_CR16","first-page":"78","volume":"91-106","author":"TH Hai","year":"2020","unstructured":"Hai, T.H.: Two modified extragradient algorithms for solving variational inequalities. J.Glob.Optim. 91-106, 78 (2020)","journal-title":"J.Glob.Optim."},{"key":"1172_CR17","doi-asserted-by":"publisher","first-page":"1051","DOI":"10.1007\/s13398-016-0347-6","volume":"111","author":"TN Hai","year":"2017","unstructured":"Hai, T.N., Vinh, N.T.: Two new splitting algorithms for equilibrium problems. RACSAM. 111, 1051\u20131069 (2017)","journal-title":"RACSAM."},{"key":"1172_CR18","doi-asserted-by":"crossref","unstructured":"He, S.N., Liu, L.L., Gibali, A.: Self-adaptive iterative method for solving boundedly Lipschitz continuous and strongly monotone variational inequalities, Journal of inequalities and applications. 350 (2018)","DOI":"10.1186\/s13660-018-1941-2"},{"key":"1172_CR19","doi-asserted-by":"publisher","first-page":"51","DOI":"10.1007\/s11784-018-0531-8","volume":"20","author":"C Kranzow","year":"2018","unstructured":"Kranzow, C., Shehu, Y.: Strong convergence of a double projection-type method for monotone variational inequalities in Hilbert spaces. J.Fixed point Theory Appl. 20, 51\u201373 (2018)","journal-title":"J.Fixed point Theory Appl."},{"key":"1172_CR20","doi-asserted-by":"publisher","first-page":"341","DOI":"10.1007\/s10898-013-0042-5","volume":"58","author":"PD Khanh","year":"2014","unstructured":"Khanh, P.D., Vuong, P.T.: Modified projection method for strongly pseudomonotone variational inequalities. J. Glob. Optim. 58, 341\u2013350 (2014)","journal-title":"J. Glob. Optim."},{"key":"1172_CR21","doi-asserted-by":"publisher","unstructured":"Ming\u00f3rski, S., Fang, C.J., Zeng, S.D.: A new modified subgradient extragradient method for solving variational inequalities Applicable Analysis. https:\/\/doi.org\/10.1080\/00036811.2019.1594202 (2019)","DOI":"10.1080\/00036811.2019.1594202"},{"key":"1172_CR22","doi-asserted-by":"publisher","first-page":"225","DOI":"10.1007\/s10107-011-0468-9","volume":"129","author":"A Nedi\u00e9c","year":"2011","unstructured":"Nedi\u00e9c, A.: Random algorithms for convex minimization problems. Math. Program. 129, 225\u2013253 (2011)","journal-title":"Math. Program."},{"key":"1172_CR23","first-page":"81","volume":"983\u20131001","author":"KA Pham","year":"2019","unstructured":"Pham, K.A., Nguyen, T.V.: Self-adaptive gradient projection algorithms for variational inequalities involving non-Lipschitz continuous operators, Numer. Algorithms. 983\u20131001, 81 (2019)","journal-title":"Algorithms."},{"key":"1172_CR24","doi-asserted-by":"publisher","first-page":"14","DOI":"10.1016\/0041-5553(69)90061-5","volume":"9","author":"BT Polyak","year":"1969","unstructured":"Polyak, B.T.: Minimization of unsmooth functionals, USSR Computat. Math. Math. Phys. 9, 14\u201329 (1969)","journal-title":"Math. Math. Phys."},{"key":"1172_CR25","doi-asserted-by":"crossref","unstructured":"Robbins, H., Siegmund, D.: A convergence theorem for nonegative almost supermartingales and some applications. In:J.S.Rustagi(ed)Optimizing Methods in Statistics, PP233-257, Academic Press, New York (1971)","DOI":"10.1016\/B978-0-12-604550-5.50015-8"},{"key":"1172_CR26","doi-asserted-by":"crossref","unstructured":"Rockafellar, R.T.: Convex analysis Princeton University Press (1970)","DOI":"10.1515\/9781400873173"},{"key":"1172_CR27","first-page":"7","volume":"65-183","author":"M Sibony","year":"1970","unstructured":"Sibony, M.: M\u00e9thodes it\u00e9ratives pour les \u00e9quations et inequations aux d\u00e9riv\u00e9es partielles nonlin\u00e9ares de type monotone. Calcolo. 65-183, 7 (1970)","journal-title":"Calcolo."},{"key":"1172_CR28","volume-title":"Shreve: Stochastic calculus for finance continuous: continuous-time models","author":"E Steven","year":"2004","unstructured":"Steven, E.: Shreve: Stochastic calculus for finance continuous: continuous-time models. Springer Science+Business Media, New York (2004)"},{"key":"1172_CR29","doi-asserted-by":"publisher","first-page":"259","DOI":"10.1007\/s11075-016-0253-1","volume":"76","author":"Y Shehu","year":"2017","unstructured":"Shehu, Y., Iyiola, O.S.: Strong convergence result for monotone variational inequalities. Numer. Algorithms. 76, 259\u2013282 (2017)","journal-title":"Numer. Algorithms."},{"key":"1172_CR30","first-page":"14","volume":"1177-1191","author":"NH Trinh","year":"2020","unstructured":"Trinh, N.H.: On gradient projection methods for strongly pseudomonotone variational inequalities without Lipschitz continuty. Optimization Letters. 1177-1191, 14 (2020)","journal-title":"Optimization Letters."},{"key":"1172_CR31","doi-asserted-by":"publisher","first-page":"1045","DOI":"10.1007\/s11075-017-0412-z","volume":"78","author":"DV Thong","year":"2018","unstructured":"Thong, D.V., Hieu, D.V.: Weak and strong convergence for variational inequality problems. Numer. Algorithms. 78, 1045\u20131060 (2018)","journal-title":"Numer. Algorithms."},{"key":"1172_CR32","first-page":"150","volume":"321\u2013363","author":"MD Wang","year":"2015","unstructured":"Wang, M.D., Bertsekas, D.P.: Incremental constraint projection methods for variational inequalities. Math. Program. 321\u2013363, 150 (2015)","journal-title":"Math. Program."},{"key":"1172_CR33","doi-asserted-by":"publisher","unstructured":"Wang, W.Y., Xia, F.Q.: Random and cyclic projection algorithms for variational inequalities, Optimization. https:\/\/doi.org\/10.1080\/02331934.2020.1829620 (2020)","DOI":"10.1080\/02331934.2020.1829620"},{"key":"1172_CR34","first-page":"3","volume":"470-502","author":"FQ Xia","year":"2017","unstructured":"Xia, F.Q., Ansari, Q.H., Yao, J.C.: A new incremental constraint projection method for solving monotone variational inequalities. Optim. Method Soft. 470-502, 3 (2017)","journal-title":"Optim. Method Soft."}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-021-01172-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11075-021-01172-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-021-01172-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,3,21]],"date-time":"2022-03-21T10:25:43Z","timestamp":1647858343000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11075-021-01172-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,8,6]]},"references-count":34,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2022,4]]}},"alternative-id":["1172"],"URL":"https:\/\/doi.org\/10.1007\/s11075-021-01172-z","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"value":"1017-1398","type":"print"},{"value":"1572-9265","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,8,6]]},"assertion":[{"value":"6 September 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 July 2021","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 August 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}