{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,4]],"date-time":"2025-06-04T02:24:37Z","timestamp":1749003877950},"reference-count":33,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2007,2,14]],"date-time":"2007-02-14T00:00:00Z","timestamp":1171411200000},"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":[[2007,9,4]]},"DOI":"10.1007\/s10898-007-9137-1","type":"journal-article","created":{"date-parts":[[2007,2,13]],"date-time":"2007-02-13T13:15:00Z","timestamp":1171372500000},"page":"247-260","source":"Crossref","is-referenced-by-count":15,"title":["An extension of gap functions for a system of vector equilibrium problems with applications to optimization problems"],"prefix":"10.1007","volume":"39","author":[{"given":"Jun","family":"Li","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nan-Jing","family":"Huang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2007,2,14]]},"reference":[{"key":"9137_CR1","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1023\/B:JOGO.0000035018.46514.ca","volume":"29","author":"Q.H. Ansari","year":"2004","unstructured":"Ansari Q.H., Chan W.K. and Yang X.Q. (2004). The system of vector quasi-equilibrium problems with applications. J. Global Optim. 29: 45\u201357","journal-title":"J. Global Optim."},{"key":"9137_CR2","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1023\/A:1013857924393","volume":"22","author":"Q.H. Ansari","year":"2002","unstructured":"Ansari Q.H., Schaible S. and Yao J.C. (2002). The system of generalized vector equilibrium problems with applications.. J. Global Optim. 22: 3\u201316","journal-title":"J. Global Optim."},{"key":"9137_CR3","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1016\/S0893-9659(99)00121-4","volume":"12","author":"Q.H. Ansari","year":"1999","unstructured":"Ansari Q.H. and Yao J.C. (1999). An existence result for generalized vector equilibrium problem. Appl. Math. Lett. 12: 53\u201356","journal-title":"Appl. Math. Lett."},{"issue":"3","key":"9137_CR4","doi-asserted-by":"crossref","first-page":"527","DOI":"10.1023\/A:1022603406244","volume":"92","author":"M. Bianchi","year":"1997","unstructured":"Bianchi M., Hadjisavvas N. and Schaible S. (1997). Vector equilibrium problems with generalized monotone bifunctions. J. Optim. Theory Appl. 92(3): 527\u2013542","journal-title":"J. Optim. Theory Appl."},{"key":"9137_CR5","first-page":"123","volume":"63","author":"E. Blum","year":"1994","unstructured":"Blum E. and Oettli W. (1994). From optimization and variational inequalities to equilibrium problems. The Math. Student 63: 123\u2013145","journal-title":"The Math. Student"},{"key":"9137_CR6","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. and Yao J.C. (2003). Equilibrium problems with applications to eigenvalue problems. J. Optim. Theory Appl. 117: 245\u2013266","journal-title":"J. Optim. Theory Appl."},{"key":"9137_CR7","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1007\/978-1-4613-0299-5_4","volume-title":"Vector Variational Inequalities and Vector Equilibrium","author":"G.Y. Chen","year":"2000","unstructured":"Chen G.Y., Goh C.J. and Yang X.Q. (2000). On gap functions for vector variational inequalities. In: Giannessi, F. (eds) Vector Variational Inequalities and Vector Equilibrium, pp 55\u201372. Kluwer Academic Publishers, Dordrecht, Boston, London"},{"key":"9137_CR8","unstructured":"Chen, G.Y., Huang, X.X., Yang, X.Q.: Vector Optimization: Set-valued and Variational Analysis. Lecture Notes in Economics and Mathematical Systems 541, Springer-Verlag, Berlin, Heidelberg (2005)"},{"issue":"1","key":"9137_CR9","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1023\/A:1013044529035","volume":"112","author":"G.Y. Chen","year":"2002","unstructured":"Chen G.Y. and Yang X.Q. (2002). Characterizations of variable domination structures via nonlinear scalarization. J. Optim. Theory Appl. 112(1): 97\u2013110","journal-title":"J. Optim. Theory Appl."},{"issue":"4","key":"9137_CR10","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1007\/s10898-003-2683-2","volume":"32","author":"G.Y. Chen","year":"2005","unstructured":"Chen G.Y., Yang X.Q. and Yu H. (2005). A nonlinear scalarization function and generalized quasi-vector equilibrium problems. J. Global Optim. 32(4): 451\u2013466","journal-title":"J. Global Optim."},{"key":"9137_CR11","doi-asserted-by":"crossref","first-page":"398","DOI":"10.1016\/j.jmaa.2004.05.039","volume":"298","author":"X.P. Ding","year":"2004","unstructured":"Ding X.P., Yao J.C. and Lin L.J. (2004). Solutions of system of generalized vector quasi-equilibrium problems in locally G-convex uniform spaces. J. Math. Anal. Appl. 298: 398\u2013410","journal-title":"J. Math. Anal. Appl."},{"key":"9137_CR12","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1023\/B:AMHU.0000028828.52601.9e","volume":"103","author":"Y.P. Fang","year":"2004","unstructured":"Fang Y.P. and Huang N.J. (2004). Existence results for systems of strong implicit vector variational inequalities. Acta Math. Hungar. 103: 265\u2013277","journal-title":"Acta Math. Hungar."},{"key":"9137_CR13","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1080\/02331930410001712652","volume":"53","author":"Y.P. Fang","year":"2004","unstructured":"Fang Y.P. and Huang N.J. (2004). Vector equilibrium type problems with (S)+-conditions. Optimization 53: 269\u2013279","journal-title":"Optimization"},{"key":"9137_CR14","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1023\/A:1024971128483","volume":"77","author":"Y.P. Flores-Baz\u00e1n","year":"2003","unstructured":"Flores-Baz\u00e1n Y.P. (2003). Existence theory for finite-dimensional pseudomonotone equilibrium problems. Acta Appl. Math. 77: 249\u2013297","journal-title":"Acta Appl. Math."},{"key":"9137_CR15","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1007\/BF00940478","volume":"67","author":"C. Gerth","year":"1990","unstructured":"Gerth C. and Weidner P. (1990). Nonconvex separation theorems and some applications in vector optimization. J. Optim. Theory Appl. 67: 297\u2013320","journal-title":"J. Optim. Theory Appl."},{"key":"9137_CR16","unstructured":"Giannessi F. Theorem of alternative, quadratic programs, and complementarity problems. In: Cottle R.W., Giannessi F., Lions J.L. (ed.) Variational Inequality and Complementarity Problems, pp. 151\u2013186. John Wiley and Sons, Chichester, England"},{"key":"9137_CR17","doi-asserted-by":"crossref","unstructured":"Giannessi, F. (ed.): Vector Variational Inequalities and Vector Equilibrium. Kluwer Academic Publishers, Dordrecht, Boston, London (2000)","DOI":"10.1007\/978-1-4613-0299-5"},{"key":"9137_CR18","doi-asserted-by":"crossref","DOI":"10.1201\/9781420018868","volume-title":"Duality in Optimization and Variational Inequalities","author":"C.J. Goh","year":"2002","unstructured":"Goh C.J. and Yang X.Q. (2002). Duality in Optimization and Variational Inequalities. Taylor and Francis, London"},{"key":"9137_CR19","volume-title":"Variational Methods in Partially Ordered Spaces","author":"A. G\u00f6pfert","year":"2003","unstructured":"G\u00f6pfert A., Riahi H., Tammer C. and Z\u0103linescu C. (2003). Variational Methods in Partially Ordered Spaces. Springer-Verlag, Berlin"},{"issue":"2","key":"9137_CR20","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1023\/A:1022666014055","volume":"96","author":"N. Hadjisavvas","year":"1998","unstructured":"Hadjisavvas N. and Schaible S. (1998). From scalar to vector equilibrium problems in the quasimonotone case. J. Optim. Theory Appl. 96(2): 297\u2013309","journal-title":"J. Optim. Theory Appl."},{"key":"9137_CR21","doi-asserted-by":"crossref","first-page":"1003","DOI":"10.1016\/S0893-9659(03)90087-5","volume":"16","author":"N.J. Huang","year":"2003","unstructured":"Huang N.J. and Gao C.J. (2003). Some generalized vector variational inequalities and complementarity problems for multivalued mappings. Appl. Math. Lett. 16: 1003\u20131010","journal-title":"Appl. Math. Lett."},{"key":"9137_CR22","doi-asserted-by":"crossref","first-page":"1343","DOI":"10.1016\/S0895-7177(03)90045-8","volume":"37","author":"N.J. Huang","year":"2003","unstructured":"Huang N.J., Li J. and Thompson H.B. (2003). Implicit vector equilibrium problems with applications. Math. Comput. Modelling 37: 1343\u20131356","journal-title":"Math. Comput. Modelling"},{"key":"9137_CR23","doi-asserted-by":"crossref","unstructured":"Huang, N.J., Li, J., Yao, J.C.: Gap functions and existence of solutions for a system of vector equilibrium problems. J. Optim. Theory Appl. (in press)","DOI":"10.1007\/s10957-007-9202-4"},{"key":"9137_CR24","volume-title":"Introduce to Global Optimization","author":"R. Horst","year":"1995","unstructured":"Horst R., Pardalos P.M. and Thoai N.V. (1995). Introduce to Global Optimization. Kluwer Academic Publishers, Dordrecht, Boston, London"},{"key":"9137_CR25","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-3623-6","volume-title":"Complementarity, Equilibrium, Efficiency and Economics","author":"G. Isac","year":"2002","unstructured":"Isac G., Bulavski V.A. and Kalashnikov V.V. (2002). Complementarity, Equilibrium, Efficiency and Economics. Kluwer Academic Publishers, Dordrecht, Boston, London"},{"issue":"9","key":"9137_CR26","doi-asserted-by":"crossref","first-page":"989","DOI":"10.1016\/j.aml.2004.06.029","volume":"18","author":"J. Li","year":"2005","unstructured":"Li J. and He Z.Q. (2005). Gap functions and existence of solutions to generalized vector variational inequalities. Appl. Math. Lett. 18(9): 989\u20131000","journal-title":"Appl. Math. Lett."},{"issue":"1","key":"9137_CR27","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1017\/S000497270003495X","volume":"72","author":"J. Li","year":"2005","unstructured":"Li J. and Huang N.J. (2005). Implicit vector equilibrium problems via nonlinear scalarisation. Bulletin of the Australian Mathematical Society 72(1): 161\u2013172","journal-title":"Bulletin of the Australian Mathematical Society"},{"key":"9137_CR28","doi-asserted-by":"crossref","first-page":"501","DOI":"10.1016\/S0022-247X(03)00277-4","volume":"283","author":"J. Li","year":"2003","unstructured":"Li J., Huang N.J. and Kim J.K. (2003). On implicit vector equilibrium problems. J. Math. Anal. Appl. 283: 501\u2013512","journal-title":"Anal. Appl."},{"key":"9137_CR29","doi-asserted-by":"crossref","first-page":"385","DOI":"10.1007\/s001860400412","volume":"61","author":"S.J. Li","year":"2005","unstructured":"Li S.J., Teo K.L. and Yang X.Q. (2005). Generalized vector quasi-equilibrium problems. Math. Meth. Oper. Res. 61: 385\u2013397","journal-title":"Math. Meth. Oper. Res."},{"key":"9137_CR30","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1007\/s10898-004-2119-7","volume":"32","author":"L.J. Lin","year":"2005","unstructured":"Lin L.J. and Chen H.L. (2005). The study of KKM theorems with applications to vector equilibrium problems and implicit vector variational inequalities problems. J. Global Optim. 32: 135\u2013157","journal-title":"J. Global Optim."},{"key":"9137_CR31","doi-asserted-by":"crossref","first-page":"411","DOI":"10.1023\/A:1026050425030","volume":"27","author":"G. Mastroeni","year":"2003","unstructured":"Mastroeni G. (2003). Gap functions for equilibrium problems. J. Global Optim. 27: 411\u2013426","journal-title":"J. Global Optim."},{"key":"9137_CR32","doi-asserted-by":"crossref","first-page":"437","DOI":"10.1023\/A:1022422407705","volume":"116","author":"X.Q. Yang","year":"2003","unstructured":"Yang X.Q. (2003). On the gap functions of prevariational inequalities. J. Optim. Theory Appl. 116: 437\u2013452","journal-title":"J. Optim. Theory Appl."},{"key":"9137_CR33","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1023\/A:1020844423345","volume":"115","author":"X.Q. Yang","year":"2002","unstructured":"Yang X.Q. and Yao J.C. (2002). Gap functions and existence of solutions to set-valued vector variational inequalities. J. Optim. Theory Appl. 115: 407\u2013417","journal-title":"J. Optim. Theory Appl."}],"container-title":["Journal of Global Optimization"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-007-9137-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10898-007-9137-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-007-9137-1","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,31]],"date-time":"2019-05-31T12:12:07Z","timestamp":1559304727000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10898-007-9137-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,2,14]]},"references-count":33,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2007,9,4]]}},"alternative-id":["9137"],"URL":"https:\/\/doi.org\/10.1007\/s10898-007-9137-1","relation":{},"ISSN":["0925-5001","1573-2916"],"issn-type":[{"value":"0925-5001","type":"print"},{"value":"1573-2916","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,2,14]]}}}