{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,14]],"date-time":"2026-03-14T19:36:30Z","timestamp":1773516990775,"version":"3.50.1"},"reference-count":29,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2008,3,8]],"date-time":"2008-03-08T00:00:00Z","timestamp":1204934400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Comput Optim Appl"],"published-print":{"date-parts":[[2010,1]]},"DOI":"10.1007\/s10589-008-9173-x","type":"journal-article","created":{"date-parts":[[2008,3,7]],"date-time":"2008-03-07T10:57:13Z","timestamp":1204887433000},"page":"89-109","source":"Crossref","is-referenced-by-count":42,"title":["Some projection-like methods for the generalized Nash equilibria"],"prefix":"10.1007","volume":"45","author":[{"given":"Jianzhong","family":"Zhang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Biao","family":"Qu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Naihua","family":"Xiu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2008,3,8]]},"reference":[{"key":"9173_CR1","doi-asserted-by":"crossref","first-page":"265","DOI":"10.2307\/1907353","volume":"22","author":"K.J. Arrow","year":"1954","unstructured":"Arrow, K.J., Debreu, G.: Existence of an equilibrium for a competitive economy. Econometrica 22, 265\u2013290 (1954)","journal-title":"Econometrica"},{"key":"9173_CR2","doi-asserted-by":"crossref","first-page":"460","DOI":"10.1137\/0312037","volume":"12","author":"A. Bensoussan","year":"1974","unstructured":"Bensoussan, A.: Points de Nash dans le cas de fontionnelles quadratiques et jeux differentiels lin\u00e9aires a N persons. SIAM J. Control 12, 460\u2013499 (1974)","journal-title":"SIAM J. Control"},{"key":"9173_CR3","first-page":"21","volume":"37","author":"J. Cash","year":"2001","unstructured":"Cash, J.: Solution set in a special case of generalized Nash equilibrium games. Kybernetika 37, 21\u201337 (2001)","journal-title":"Kybernetika"},{"key":"9173_CR4","volume-title":"Researches into the Mathematical Principles of the Theory of Wealth","author":"A.A. Cournot","year":"1897","unstructured":"Cournot, A.A.: Researches into the Mathematical Principles of the Theory of Wealth. Macmillan, New York (1897)"},{"key":"9173_CR5","volume-title":"Finite-Dimensional Variational Inequality and Complementarity Problems","author":"F. Facchinei","year":"2003","unstructured":"Facchinei, F., Pang, J.S.: Finite-Dimensional Variational Inequality and Complementarity Problems. Springer, New York (2003)"},{"key":"9173_CR6","first-page":"99","volume":"53","author":"E.M. Gafni","year":"1984","unstructured":"Gafni, E.M., Bertsekas, D.P.: Two-metric projection problems and descent methods for asymmetric variational inequality problems. Math. Program. 53, 99\u2013110 (1984)","journal-title":"Math. Program."},{"key":"9173_CR7","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1016\/0377-2217(91)90325-P","volume":"54","author":"P.T. Harker","year":"1991","unstructured":"Harker, P.T.: Generalized Nash games and quasi-variational inequalities. Eur. J. Oper. Res. 54, 81\u201394 (1991)","journal-title":"Eur. J. Oper. Res."},{"key":"9173_CR8","first-page":"103","volume":"13","author":"A.N. Iusem","year":"1994","unstructured":"Iusem, A.N.: An iterative algorithm for the variational inequality problem. Math. Appl. Comput. 13, 103\u2013114 (1994)","journal-title":"Math. Appl. Comput."},{"key":"9173_CR9","doi-asserted-by":"crossref","first-page":"120","DOI":"10.1016\/0041-5553(87)90058-9","volume":"17","author":"E.N. Khobotov","year":"1987","unstructured":"Khobotov, E.N.: Modification of the extragradient method for solving variational inequalities and certain optimization problem. U.S.S.R. Comput. Math. Math. Phys. 17, 120\u2013127 (1987)","journal-title":"U.S.S.R. Comput. Math. Math. Phys."},{"key":"9173_CR10","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1080\/10556789508805617","volume":"5","author":"M. Kocvara","year":"1995","unstructured":"Kocvara, M., Outrata, J.V.: On a class of quasi-variational inequalities. Optim. Methods Software 5, 275\u2013295 (1995)","journal-title":"Optim. Methods Software"},{"key":"9173_CR11","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. Matecon 12, 747\u2013756 (1976)","journal-title":"Matecon"},{"key":"9173_CR12","first-page":"258","volume":"29","author":"P. Marcotte","year":"1991","unstructured":"Marcotte, P.: Application of Khobotov\u2019s algorithm to variational inequalities and network equilibrium problems. Inf. Syst. Oper. Res. 29, 258\u2013270 (1991)","journal-title":"Inf. Syst. Oper. Res."},{"key":"9173_CR13","doi-asserted-by":"crossref","first-page":"54","DOI":"10.2307\/1907777","volume":"27","author":"L.W. McKenzie","year":"1959","unstructured":"McKenzie, L.W.: On the existence of general equilibrium for a competitive market. Econometrica 27, 54\u201371 (1959)","journal-title":"Econometrica"},{"key":"9173_CR14","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1073\/pnas.36.1.48","volume":"36","author":"J.F. Nash","year":"1950","unstructured":"Nash, J.F.: Equilibrium points in n-person games. Proc. Nat. Acad. Sci. U.S.A. 36, 48\u201349 (1950)","journal-title":"Proc. Nat. Acad. Sci. U.S.A."},{"key":"9173_CR15","doi-asserted-by":"crossref","first-page":"286","DOI":"10.2307\/1969529","volume":"54","author":"J.F. Nash","year":"1951","unstructured":"Nash, J.F.: Non-cooperative games. Ann. Math. 54, 286\u2013295 (1951)","journal-title":"Ann. Math."},{"key":"9173_CR16","first-page":"105","volume":"68","author":"J. Outrata","year":"1995","unstructured":"Outrata, J., Zowe, J.: A numerical approach to optimization problems with variational inequality constraints. Math. Program. 68, 105\u2013130 (1995)","journal-title":"Math. Program."},{"key":"9173_CR17","unstructured":"Pang, J.S.: Computing generalized Nash equilibria. Department of Mathematical sciences, The Johns Hopkins University (2002). Manuscript"},{"key":"9173_CR18","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1007\/s10287-004-0010-0","volume":"2","author":"J.S. Pang","year":"2005","unstructured":"Pang, J.S., Fukushima, M.: Quasi-variational inequalities, generalized Nash equilibria, and multi-leader-follower games. Comput. Manage. Sci. 2, 21\u201356 (2005)","journal-title":"Comput. Manage. Sci."},{"key":"9173_CR19","doi-asserted-by":"crossref","first-page":"518","DOI":"10.1287\/opre.41.3.518","volume":"41","author":"S.M. Robinson","year":"1993","unstructured":"Robinson, S.M.: Shadow prices for measures of effectiveness. I. Linear Model. Oper. Res. 41, 518\u2013535 (1993)","journal-title":"Oper. Res."},{"key":"9173_CR20","doi-asserted-by":"crossref","first-page":"536","DOI":"10.1287\/opre.41.3.536","volume":"41","author":"S.M. Robinson","year":"1993","unstructured":"Robinson, S.M.: Shadow prices for measures of effectiveness. II. General Model. Oper. Res. 41, 536\u2013548 (1993)","journal-title":"Oper. Res."},{"key":"9173_CR21","first-page":"145","volume":"16","author":"D. Sun","year":"1994","unstructured":"Sun, D.: An iterative method for solving variational inequality problems and complementarity problems. Numer. Math. J. Chin. Univ. 16, 145\u2013153 (1994)","journal-title":"Numer. Math. J. Chin. Univ."},{"key":"9173_CR22","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1093\/imanum\/8.2.231","volume":"8","author":"Ph.L. Toint","year":"1988","unstructured":"Toint, Ph.L.: Global convergence of a class of trust region methods for nonconvex minimization in Hilbert space. IMA J. Numer. Anal. 8, 231\u2013252 (1988)","journal-title":"IMA J. Numer. Anal."},{"key":"9173_CR23","author":"A. Heusinger von","year":"2007","unstructured":"von Heusinger, A., Kanzow, C.: Optimization reformulations of the generalized Nash equilibrium problem using Nikaido-Isoda-type functions. Comput. Optim. Appl. (2007). doi: 10.1007\/s10589-007-9145-6","journal-title":"Comput. Optim. Appl."},{"key":"9173_CR24","volume-title":"Theory of Games and Economic Behavior","author":"J. Neumann von","year":"1944","unstructured":"von Neumann, J., Morgenstern, O.: Theory of Games and Economic Behavior. Princeton University Press, Princeton (1944)"},{"key":"9173_CR25","doi-asserted-by":"crossref","first-page":"969","DOI":"10.1016\/S0898-1221(01)00213-9","volume":"42","author":"Y.J. Wang","year":"2001","unstructured":"Wang, Y.J., Xiu, N.H., Wang, C.Y.: A new version of extragradient method for variational inequality problems. Comput. Math. Appl. 42, 969\u2013979 (2001)","journal-title":"Comput. Math. Appl."},{"key":"9173_CR26","doi-asserted-by":"crossref","first-page":"102","DOI":"10.1287\/opre.47.1.102","volume":"47","author":"J.Y. Wei","year":"1999","unstructured":"Wei, J.Y., Smeers, Y.: Spatial oligopolistic electricity models with Cournot generators and regulated transmission prices. Oper. Res. 47, 102\u2013112 (1999)","journal-title":"Oper. Res."},{"key":"9173_CR27","doi-asserted-by":"crossref","first-page":"559","DOI":"10.1016\/S0377-0427(02)00730-6","volume":"152","author":"N.H. Xiu","year":"2003","unstructured":"Xiu, N.H., Zhang, J.Z.: Some recent advances in projection-type methods for variational inequalities. J. Comput. Appl. Math. 152, 559\u2013585 (2003)","journal-title":"J. Comput. Appl. Math."},{"key":"9173_CR28","doi-asserted-by":"crossref","first-page":"913","DOI":"10.1016\/S0898-1221(04)90075-2","volume":"47","author":"N.H. Xiu","year":"2004","unstructured":"Xiu, N.H., Wang, Y.J., Zhang, X.S.: Modified fixed-point equations and related iterative methods for variational inequalities. Comput. Math. Appl. 47, 913\u2013920 (2004)","journal-title":"Comput. Math. Appl."},{"key":"9173_CR29","volume-title":"Contributions to Nonlinear Functional Analysis","author":"E.H. Zarantonello","year":"1971","unstructured":"Zarantonello, E.H.: Projections on convex sets in Hilbert space and spectral theory. In: Zarantonello, E.H. (ed.) Contributions to Nonlinear Functional Analysis. Academic Press, New York (1971)"}],"container-title":["Computational Optimization and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-008-9173-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10589-008-9173-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-008-9173-x","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,31]],"date-time":"2019-05-31T07:36:34Z","timestamp":1559288194000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10589-008-9173-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,3,8]]},"references-count":29,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2010,1]]}},"alternative-id":["9173"],"URL":"https:\/\/doi.org\/10.1007\/s10589-008-9173-x","relation":{},"ISSN":["0926-6003","1573-2894"],"issn-type":[{"value":"0926-6003","type":"print"},{"value":"1573-2894","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,3,8]]}}}