{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,4]],"date-time":"2026-07-04T13:08:14Z","timestamp":1783170494490,"version":"3.54.6"},"reference-count":12,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2010,10,15]],"date-time":"2010-10-15T00:00:00Z","timestamp":1287100800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Optim Theory Appl"],"published-print":{"date-parts":[[2011,2]]},"DOI":"10.1007\/s10957-010-9757-3","type":"journal-article","created":{"date-parts":[[2010,10,14]],"date-time":"2010-10-14T20:21:50Z","timestamp":1287087710000},"page":"318-335","source":"Crossref","is-referenced-by-count":762,"title":["The Subgradient Extragradient Method for Solving Variational Inequalities in Hilbert Space"],"prefix":"10.1007","volume":"148","author":[{"given":"Y.","family":"Censor","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"A.","family":"Gibali","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"S.","family":"Reich","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2010,10,15]]},"reference":[{"key":"9757_CR1","first-page":"747","volume":"12","author":"G.M. Korpelevich","year":"1976","unstructured":"Korpelevich, G.M.: The extragradient method for finding saddle points and other problems. Ekon. Mat. Metody 12, 747\u2013756 (1976)","journal-title":"Ekon. Mat. Metody"},{"key":"9757_CR2","volume-title":"Finite-Dimensional Variational Inequalities and Complementarity Problems, vols.\u00a0I and\u00a0II","author":"F. Facchinei","year":"2003","unstructured":"Facchinei, F., Pang, J.S.: Finite-Dimensional Variational Inequalities and Complementarity Problems, vols.\u00a0I and\u00a0II. Springer, New York (2003)"},{"key":"9757_CR3","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1080\/02331939708844365","volume":"42","author":"A.N. Iusem","year":"1997","unstructured":"Iusem, A.N., Svaiter, B.F.: A variant of Korpelevich\u2019s method for variational inequalities with a new search strategy. Optimization 42, 309\u2013321 (1997)","journal-title":"Optimization"},{"key":"9757_CR4","doi-asserted-by":"crossref","first-page":"120","DOI":"10.1016\/0041-5553(87)90058-9","volume":"27","author":"E.N. Khobotov","year":"1989","unstructured":"Khobotov, E.N.: Modification of the extra-gradient method for solving variational inequalities and certain optimization problems. USSR Comput. Math. Math. Phys. 27, 120\u2013127 (1989)","journal-title":"USSR Comput. Math. Math. Phys."},{"key":"9757_CR5","doi-asserted-by":"crossref","first-page":"765","DOI":"10.1137\/S0363012997317475","volume":"37","author":"M.V. Solodov","year":"1999","unstructured":"Solodov, M.V., Svaiter, B.F.: A new projection method for variational inequality problems. SIAM J. Control Optim. 37, 765\u2013776 (1999)","journal-title":"SIAM J. Control Optim."},{"key":"9757_CR6","doi-asserted-by":"crossref","unstructured":"Censor, Y., Gibali, A., Reich, S.: Two extensions of Korpelevich\u2019s extragradient method for solving the variational inequality problem in Euclidean space. Technical Report (2010)","DOI":"10.1007\/s10957-010-9757-3"},{"key":"9757_CR7","volume-title":"Uniform Convexity, Hyperbolic Geometry, and Nonexpansive Mappings","author":"K. Goebel","year":"1984","unstructured":"Goebel, K., Reich, S.: Uniform Convexity, Hyperbolic Geometry, and Nonexpansive Mappings. Dekker, New York and Basel (1984)"},{"key":"9757_CR8","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1090\/S0002-9947-1970-0282272-5","volume":"149","author":"R.T. Rockafellar","year":"1970","unstructured":"Rockafellar, R.T.: On the maximality of sums of nonlinear monotone operators. Trans. Am. Math. Soc. 149, 75\u201388 (1970)","journal-title":"Trans. Am. Math. Soc."},{"key":"9757_CR9","doi-asserted-by":"crossref","first-page":"591","DOI":"10.1090\/S0002-9904-1967-11761-0","volume":"73","author":"Z. Opial","year":"1967","unstructured":"Opial, Z.: Weak convergence of the sequence of successive approximations for nonexpansive mappings. Bull. Am. Math. Soc. 73, 591\u2013597 (1967)","journal-title":"Bull. Am. Math. Soc."},{"key":"9757_CR10","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1023\/A:1025407607560","volume":"118","author":"W. Takahashi","year":"2003","unstructured":"Takahashi, W., Toyoda, M.: Weak convergence theorems for nonexpansive mappings and monotone mappings. J. Optim. Theory Appl. 118, 417\u2013428 (2003)","journal-title":"J. Optim. Theory Appl."},{"key":"9757_CR11","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1007\/s10957-005-7564-z","volume":"128","author":"N. Nadezhkina","year":"2006","unstructured":"Nadezhkina, N., Takahashi, W.: Weak convergence theorem by an extragradient method for nonexpansive mappings and monotone mappings. J. Optim. Theory Appl. 128, 191\u2013201 (2006)","journal-title":"J. Optim. Theory Appl."},{"key":"9757_CR12","doi-asserted-by":"crossref","first-page":"1272","DOI":"10.1073\/pnas.53.6.1272","volume":"53","author":"F.E. Browder","year":"1965","unstructured":"Browder, F.E.: Fixed point theorems for noncompact mappings in Hilbert space. Proc. Natl. Acad. Sci. USA 53, 1272\u20131276 (1965)","journal-title":"Proc. Natl. Acad. Sci. USA"}],"container-title":["Journal of Optimization Theory and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-010-9757-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10957-010-9757-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-010-9757-3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,6,3]],"date-time":"2023-06-03T20:53:56Z","timestamp":1685825636000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10957-010-9757-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,10,15]]},"references-count":12,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2011,2]]}},"alternative-id":["9757"],"URL":"https:\/\/doi.org\/10.1007\/s10957-010-9757-3","relation":{},"ISSN":["0022-3239","1573-2878"],"issn-type":[{"value":"0022-3239","type":"print"},{"value":"1573-2878","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,10,15]]}}}