{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,11]],"date-time":"2026-02-11T18:58:28Z","timestamp":1770836308772,"version":"3.50.1"},"reference-count":36,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2012,9,21]],"date-time":"2012-09-21T00:00:00Z","timestamp":1348185600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Glob Optim"],"published-print":{"date-parts":[[2013,11]]},"DOI":"10.1007\/s10898-012-9982-4","type":"journal-article","created":{"date-parts":[[2012,9,20]],"date-time":"2012-09-20T09:25:59Z","timestamp":1348133159000},"page":"935-950","source":"Crossref","is-referenced-by-count":2,"title":["Superimposed optimization methods for the mixed equilibrium problem and variational inclusion"],"prefix":"10.1007","volume":"57","author":[{"given":"Yonghong","family":"Yao","sequence":"first","affiliation":[]},{"given":"Yeong-Cheng","family":"Liou","sequence":"additional","affiliation":[]},{"given":"Ngai-Ching","family":"Wong","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2012,9,21]]},"reference":[{"key":"9982_CR1","first-page":"123","volume":"63","author":"E. Blum","year":"1994","unstructured":"Blum E., Oettli W.: From optimization and variational inequalities to equilibrium problems. Math. Stud. 63, 123\u2013145 (1994)","journal-title":"Math. Stud."},{"key":"9982_CR2","doi-asserted-by":"crossref","first-page":"967","DOI":"10.1016\/j.cam.2008.03.032","volume":"223","author":"L.C. Ceng","year":"2009","unstructured":"Ceng L.C., Al-Homidan S., Ansari Q.H., Yao J.C.: An iterative scheme for equilibrium problems and fixed point problems of strict pseudocontraction mappings. J. Comput. Appl. Math. 223, 967\u2013974 (2009)","journal-title":"J. Comput. Appl. Math."},{"issue":"383740","key":"9982_CR3","first-page":"19","volume":"2010","author":"F. Cianciaruso","year":"2010","unstructured":"Cianciaruso F., Marino G., Muglia L., Yao Y.: A hybrid projection algorithm for finding solutions of mixed equilibrium problem and variational inequality problem. Fixed Point Theory Appl. 2010(383740), 19 (2010)","journal-title":"Fixed Point Theory Appl."},{"key":"9982_CR4","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1023\/A:1023627606067","volume":"117","author":"O. Chadli","year":"2003","unstructured":"Chadli O., Wong N.C., Yao J.C.: Equilibrium problems with applications to eigenvalue problems. J. Optim. Theory Appl. 117, 245\u2013266 (2003)","journal-title":"J. Optim. Theory Appl."},{"key":"9982_CR5","doi-asserted-by":"crossref","first-page":"3513","DOI":"10.1016\/j.na.2010.07.011","volume":"73","author":"V. Colao","year":"2010","unstructured":"Colao V., Marino G.: Strong convergence for a minimization problem on points of equilibrium and common fixed points of an infinite family of nonexpansive mappings. Nonlinear Anal. 73, 3513\u20133524 (2010)","journal-title":"Nonlinear Anal."},{"key":"9982_CR6","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1016\/S0025-5610(96)00071-8","volume":"78","author":"P.L. Combettes","year":"1997","unstructured":"Combettes P.L., Hirstoaga S.A.: Equilibrium programming using proximal-like algorithms. Math. Program. 78, 29\u201341 (1997)","journal-title":"Math. Program."},{"key":"9982_CR7","first-page":"117","volume":"6","author":"P.L. Combettes","year":"2005","unstructured":"Combettes P.L., Hirstoaga A.: Equilibrium programming in Hilbert spaces. J. Nonlinear Convex Anal. 6, 117\u2013136 (2005)","journal-title":"J. Nonlinear Convex Anal."},{"key":"9982_CR8","volume-title":"Equilibrium Problems and Variational Models","author":"F. Giannessi","year":"2001","unstructured":"Giannessi F., Maugeri A., Pardalos P.M.: Equilibrium Problems and Variational Models. Kluwer, Dordrecht (2001)"},{"key":"9982_CR9","volume-title":"New Trends in Equilibrium Systems","author":"F. Giannessi","year":"2001","unstructured":"Giannessi F., Pardalos P.M., Rapcsak T.: New Trends in Equilibrium Systems. Kluwer, Dordrecht (2001)"},{"key":"9982_CR10","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4613-0287-2","volume-title":"From Convexity to Nonconvexity","author":"R.P. Gilbert","year":"2001","unstructured":"Gilbert R.P., Panagiotopoulos P.D., Pardalos P.M.: From Convexity to Nonconvexity. Kluwer, Dordrecht (2001)"},{"key":"9982_CR11","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1007\/s10957-005-4716-0","volume":"126","author":"I.V. Konnov","year":"2005","unstructured":"Konnov I.V., Schaible S., Yao J.C.: Combined relaxation method for mixed equilibrium problems. J. Optim. Theory Appl. 126, 309\u2013322 (2005)","journal-title":"J. Optim. Theory Appl."},{"key":"9982_CR12","first-page":"37","volume":"9","author":"A. Moudafi","year":"2008","unstructured":"Moudafi A.: Weak convergence theorems for nonexpansive mappings and equilibrium problems. J. Nonlinear Convex Anal. 9, 37\u201343 (2008)","journal-title":"J. Nonlinear Convex Anal."},{"key":"9982_CR13","doi-asserted-by":"crossref","unstructured":"Moudafi, A., Th\u00e9ra, M.: Proximal and dynamical approaches to equilibrium problems. In: Lecture Notes in Economics and Mathematical Systems, vol. 477, Springer, pp. 187\u2013201 (1999)","DOI":"10.1007\/978-3-642-45780-7_12"},{"key":"9982_CR14","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":"9982_CR15","first-page":"313","volume":"49","author":"M.A. Noor","year":"1994","unstructured":"Noor M.A., Oettli W.: On general nonlinear complementarity problems and quasi equilibria. Mathematiche (Catania) 49, 313\u2013331 (1994)","journal-title":"Mathematiche (Catania)"},{"issue":"720371","key":"9982_CR16","first-page":"15","volume":"2008","author":"J.W. Peng","year":"2008","unstructured":"Peng J.W., Wang Y., Shyu D.S., Yao J.C.: Common solutions of an iterative scheme for variational inclusions, equilibrium problems and fixed point problems. J. Inequal. Appl. 2008(720371), 15 (2008)","journal-title":"J. Inequal. Appl."},{"key":"9982_CR17","doi-asserted-by":"crossref","first-page":"1401","DOI":"10.11650\/twjm\/1500405033","volume":"12","author":"J.W. Peng","year":"2008","unstructured":"Peng J.W., Yao J.C.: A new hybrid-extragradient method for generalized mixed equilibrium problems and fixed point problems and variational inequality problems. Taiwan. J. Math. 12, 1401\u20131433 (2008)","journal-title":"Taiwan. J. Math."},{"key":"9982_CR18","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1016\/j.na.2009.06.042","volume":"72","author":"X. Qin","year":"2010","unstructured":"Qin X., Cho Y.J., Kang S.M.: Viscosity approximation methods for generalized equilibrium problems and fixed point problems with applications. Nonlinear Anal. 72, 99\u2013112 (2010)","journal-title":"Nonlinear Anal."},{"key":"9982_CR19","doi-asserted-by":"crossref","first-page":"128","DOI":"10.1007\/BFb0120850","volume":"10","author":"S.M. Robinson","year":"1979","unstructured":"Robinson S.M.: Generalized equation and their solutions, part I: basic theory. Math Program. Study 10, 128\u2013141 (1979)","journal-title":"Math Program. Study"},{"key":"9982_CR20","doi-asserted-by":"crossref","first-page":"877","DOI":"10.1137\/0314056","volume":"14","author":"R.T. Rockafella","year":"1976","unstructured":"Rockafella R.T.: Monotone operators and the proximal point algorithm. SIAM J. Control Optim. 14, 877\u2013898 (1976)","journal-title":"SIAM J. Control Optim."},{"key":"9982_CR21","doi-asserted-by":"crossref","first-page":"1723","DOI":"10.1016\/j.camwa.2011.06.014","volume":"62","author":"S. Saewan","year":"2011","unstructured":"Saewan S., Kumam P.: A modified hybrid projection method for solving generalized mixed equilibrium problems and fixed point problems in Banach spaces. Comput. Math. Appl. 62, 1723\u20131735 (2011)","journal-title":"Comput. Math. Appl."},{"key":"9982_CR22","doi-asserted-by":"crossref","first-page":"2259","DOI":"10.1016\/j.mcm.2011.05.035","volume":"54","author":"Y. Shehu","year":"2011","unstructured":"Shehu Y.: Strong convergence theorems for nonlinear mappings, variational inequality problems and system of generalized mixed equilibrium problems. Math. Comput. Model. 54, 2259\u20132276 (2011)","journal-title":"Math. Comput. Model."},{"key":"9982_CR23","doi-asserted-by":"crossref","first-page":"506","DOI":"10.1016\/j.jmaa.2006.08.036","volume":"331","author":"S. Takahashi","year":"2007","unstructured":"Takahashi S., Takahashi W.: Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces. J. Math. Anal. Appl. 331, 506\u2013515 (2007)","journal-title":"J. Math. Anal. Appl."},{"key":"9982_CR24","doi-asserted-by":"crossref","first-page":"1025","DOI":"10.1016\/j.na.2008.02.042","volume":"69","author":"S. Takahashi","year":"2008","unstructured":"Takahashi S., Takahashi W.: Strong convergence theorem for a generalized equilibrium problem and a nonexpansive mapping in a Hilbert space. Nonlinear Anal. 69, 1025\u20131033 (2008)","journal-title":"Nonlinear Anal."},{"key":"9982_CR25","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1007\/s10957-010-9713-2","volume":"147","author":"S. Takahashi","year":"2010","unstructured":"Takahashi S., Takahashi W., Toyoda M.: Strong convergence theorems for maximal monotone operators with nonlinear mappings in Hilbert spaces. J. Optim. Theory Appl. 147, 27\u201341 (2010)","journal-title":"J. Optim. Theory Appl."},{"key":"9982_CR26","doi-asserted-by":"crossref","first-page":"240","DOI":"10.1112\/S0024610702003332","volume":"66","author":"H.K. Xu","year":"2002","unstructured":"Xu H.K.: Iterative algorithms for nonlinear operators. J. Lond. Math. Soc. 66, 240\u2013256 (2002)","journal-title":"J. Lond. Math. Soc."},{"key":"9982_CR27","doi-asserted-by":"crossref","first-page":"3363","DOI":"10.1016\/j.na.2009.01.236","volume":"71","author":"Y. Yao","year":"2009","unstructured":"Yao Y., Cho Y.J., Chen R.: An iterative algorithm for solving fixed point problems, variational inequality problems and mixed equilibrium problems. Nonlinear Anal. 71, 3363\u20133373 (2009)","journal-title":"Nonlinear Anal."},{"key":"9982_CR28","doi-asserted-by":"crossref","first-page":"242","DOI":"10.1016\/j.ejor.2011.01.042","volume":"212","author":"Y. Yao","year":"2011","unstructured":"Yao Y., Cho Y.J., Liou Y.C.: Algorithms of common solutions for variational inclusions, mixed equilibrium problems and fixed point problems. Eur. J. Oper. Res. 212, 242\u2013250 (2011)","journal-title":"Eur. J. Oper. Res."},{"key":"9982_CR29","doi-asserted-by":"crossref","unstructured":"Yao, Y., Liou, Y.C.: Composite algorithms for minimization over the solutions of equilibrium problems and fixed point problems. Abstr. Appl. Anal. Article ID 763506, 19\u00a0pp. (2010). doi: 10.1155\/2010\/763506 .","DOI":"10.1155\/2010\/763506"},{"key":"9982_CR30","doi-asserted-by":"crossref","unstructured":"Yao, Y., Liou, Y.C., Yao, J.C.: Convergence theorem for equilibrium problems and fixed point problems of infinite family of nonexpansive mappings. Fixed Point Theory Appl. Article ID 64363, 12\u00a0pp. (2007)","DOI":"10.1155\/2007\/64363"},{"issue":"3","key":"9982_CR31","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1080\/02331930903196941","volume":"60","author":"Y. Yao","year":"2011","unstructured":"Yao Y., Liou Y.C., Yao J.C.: New relaxed hybrid extragradient method for fixed point problems, a general system of variational inequality problems and generalized mixed equilibrium problems. Optimization 60(3), 395\u2013412 (2011)","journal-title":"Optimization"},{"key":"9982_CR32","doi-asserted-by":"crossref","first-page":"497","DOI":"10.1016\/j.na.2007.12.021","volume":"70","author":"Y. Yao","year":"2009","unstructured":"Yao Y., Noor M.A., Liou Y.C.: On iterative methods for equilibrium problems. Nonlinear Anal. 70, 497\u2013507 (2009)","journal-title":"Nonlinear Anal."},{"key":"9982_CR33","doi-asserted-by":"crossref","first-page":"1351","DOI":"10.1016\/j.camwa.2010.06.016","volume":"60","author":"Y. Yao","year":"2010","unstructured":"Yao Y., Noor M.A., Liou Y.C., Kang S.M.: Some new algorithms for solving mixed equilibrium problems. Comput. Math. Appl. 60, 1351\u20131359 (2010)","journal-title":"Comput. Math. Appl."},{"key":"9982_CR34","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1016\/j.jmaa.2008.12.055","volume":"354","author":"Y. Yao","year":"2009","unstructured":"Yao Y., Noor M.A., Zainab S., Liou Y.C.: Mixed equilibrium problems and optimization problems. J. Math. Anal. Appl. 354, 319\u2013329 (2009)","journal-title":"J. Math. Anal. Appl."},{"key":"9982_CR35","doi-asserted-by":"crossref","first-page":"186","DOI":"10.1016\/j.cam.2007.02.022","volume":"214","author":"L.C. Zeng","year":"2008","unstructured":"Zeng L.C., Yao J.C.: A hybrid iterative scheme for mixed equilibrium problems and fixed point problems. J. Comput. Appl. Math. 214, 186\u2013201 (2008)","journal-title":"J. Comput. Appl. Math."},{"key":"9982_CR36","doi-asserted-by":"crossref","first-page":"571","DOI":"10.1007\/s10483-008-0502-y","volume":"29","author":"S.S. Zhang","year":"2008","unstructured":"Zhang S.S., Lee J.H.W., Chan C.K.: Algorithms of common solutions for quasi variational inclusion and fixed point problems. Appl. Math. Mech. Engl. Ed. 29, 571\u2013581 (2008)","journal-title":"Appl. Math. Mech. Engl. Ed."}],"container-title":["Journal of Global Optimization"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-012-9982-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10898-012-9982-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-012-9982-4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,7,4]],"date-time":"2019-07-04T02:59:26Z","timestamp":1562209166000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10898-012-9982-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,9,21]]},"references-count":36,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2013,11]]}},"alternative-id":["9982"],"URL":"https:\/\/doi.org\/10.1007\/s10898-012-9982-4","relation":{},"ISSN":["0925-5001","1573-2916"],"issn-type":[{"value":"0925-5001","type":"print"},{"value":"1573-2916","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,9,21]]}}}