{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T12:38:26Z","timestamp":1773405506657,"version":"3.50.1"},"reference-count":11,"publisher":"Springer Science and Business Media LLC","issue":"1-4","license":[{"start":{"date-parts":[[2005,1,1]],"date-time":"2005-01-01T00:00:00Z","timestamp":1104537600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Ann Oper Res"],"published-print":{"date-parts":[[2005,1]]},"DOI":"10.1007\/s10479-004-5027-9","type":"journal-article","created":{"date-parts":[[2005,2,18]],"date-time":"2005-02-18T13:45:20Z","timestamp":1108734320000},"page":"119-125","source":"Crossref","is-referenced-by-count":11,"title":["A Relaxed Approximate Proximal Point Algorithm"],"prefix":"10.1007","volume":"133","author":[{"given":"Zhenhua","family":"Yang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bingsheng","family":"He","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"5385027_CR1","volume-title":"Op\u00e9rateurs maximaux monotone et semi-groups de contractions dans les espaces de Hilbert","author":"H. Br\u00e9zis","year":"1973","unstructured":"Br\u00e9zis, H. (1973). Op\u00e9rateurs maximaux monotone et semi-groups de contractions dans les espaces de Hilbert. Amsterdam: North-Holland."},{"key":"5385027_CR2","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1023\/A:1008615624787","volume":"5","author":"R.S. Burachik","year":"1997","unstructured":"Burachik, R.S., A.N. Iusem, and B.F. Svaiter. (1997). \u201cEnlargement of Monotone Operators with Applications to Variational Inequalities.\u201d Set-Valued Analysis 5, 159\u2013180.","journal-title":"Set-Valued Analysis"},{"key":"5385027_CR3","doi-asserted-by":"crossref","first-page":"202","DOI":"10.1287\/moor.18.1.202","volume":"18","author":"J. Eckstein","year":"1993","unstructured":"Eckstein, J. (1993). \u201cNonliear Proximal Point Algorithms Using Bregman Functions, with Applications to Convex Programming.\u201d Mathematics of Operations Research 18, 202\u2013226.","journal-title":"Mathematics of Operations Research"},{"key":"5385027_CR4","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1007\/BF01581204","volume":"55","author":"J. Eckstein","year":"1992","unstructured":"Eckstein, J. and D.P. Bertsekas. (1992). \u201cOn the Douglas\u2013Rachford Splitting method and the Proximal Points Algorithm for Maximal Monotone Operators.\u201d Mathematical Programming 55, 293\u2013318.","journal-title":"Mathematical Programming"},{"key":"5385027_CR5","first-page":"113","volume":"83","author":"J. Eckstein","year":"1998","unstructured":"Eckstein, J. (1998). \u201cApproximate Iterations in Bregman-Function-Based Proximal Algorithms.\u201d Mathematical Programming 83, 113\u2013123.","journal-title":"Mathematical Programming"},{"key":"5385027_CR6","doi-asserted-by":"crossref","first-page":"669","DOI":"10.1137\/S0036144595285963","volume":"39","author":"M.C. Ferris","year":"1997","unstructured":"Ferris, M.C. and J.S. Pang. (1997). \u201cEngineering and Economic Applications of Complementarity Problems.\u201d SIAM Review 39, 669\u2013713.","journal-title":"SIAM Review"},{"key":"5385027_CR7","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-12613-4","volume-title":"Numerical Methods for Nonlinear Variational Problems","author":"R. Glowinski","year":"1984","unstructured":"Glowinski, R. (1984). Numerical Methods for Nonlinear Variational Problems. New York: Springer."},{"key":"5385027_CR8","first-page":"243","volume":"263","author":"D.R. Han","year":"2001","unstructured":"Han, D.R. and B.S. He. (2001). \u201cA New Accuracy Criterion for Approximate Proximal Point Algorithms.\u201d Journal of Mathematical Analysis and Applications 263, 243\u2013254.","journal-title":"Journal of Mathematical Analysis and Applications"},{"key":"5385027_CR9","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1007\/s101070050086","volume":"86","author":"B.S. He","year":"1999","unstructured":"He, B.S. (1999). \u201cInexact Implicit Methods for Monotone General Variational Inequalities.\u201d Mathematical Programming 86, 199\u2013216.","journal-title":"Mathematical Programming"},{"key":"5385027_CR10","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1007\/BF00927673","volume":"4","author":"M.R. Hestenes","year":"1969","unstructured":"Hestenes, M.R. (1969) \u201cMultiplier and Gradient Methods.\u201d Journal of Optimization Theory and Applications 4, 303\u2013320.","journal-title":"Journal of Optimization Theory and Applications"},{"key":"5385027_CR11","doi-asserted-by":"crossref","first-page":"877","DOI":"10.1137\/0314056","volume":"14","author":"R.T. Rockafellar","year":"1976","unstructured":"Rockafellar, R.T. (1976). \u201cMonotone Operators and the Proximal Point Algorithm.\u201d SIAM Journal on Control and Optimization 14, 877\u2013898.","journal-title":"SIAM Journal on Control and Optimization"}],"container-title":["Annals of Operations Research"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-004-5027-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10479-004-5027-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-004-5027-9","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,29]],"date-time":"2019-05-29T13:59:33Z","timestamp":1559138373000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10479-004-5027-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,1]]},"references-count":11,"journal-issue":{"issue":"1-4","published-print":{"date-parts":[[2005,1]]}},"alternative-id":["5385027"],"URL":"https:\/\/doi.org\/10.1007\/s10479-004-5027-9","relation":{},"ISSN":["0254-5330","1572-9338"],"issn-type":[{"value":"0254-5330","type":"print"},{"value":"1572-9338","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,1]]}}}