zbMATH — the first resource for mathematics

Recession methods for generalized vector equilibrium problems. (English) Zbl 1107.49007
The authors consider vector equilibrium problems with multi-valued bifunctions in reflexive Banach spaces. By using the recession cone technique, they present several sufficient conditions for existence of solutions and show that these conditions are necessary under pseudomonotonicity type assumptions. The results can be viewed as extensions of those in the paper by F. Flores-Bazán and F. Flores-Bazán [J. Glob. Optim. 26, 141–166 (2003; Zbl 1036.90060)] from the single-valued case.

49J40 Variational inequalities
47J20 Variational and other types of inequalities involving nonlinear operators (general)
90C29 Multi-objective and goal programming
49J53 Set-valued and variational analysis
Full Text: DOI
[1] Ansari, Q.H.; Konnov, I.V.; Yao, J.C., On generalized vector equilibrium problems, Nonlinear anal., 47, 543-554, (2001) · Zbl 1042.90642
[2] Ansari, Q.H.; Konnov, I.V.; Yao, J.C., Existence of a solution and variational principles for vector equilibrium problems, J. optim. theory appl., 110, 481-492, (2001) · Zbl 0988.49004
[3] Ansari, Q.H.; Konnov, I.V.; Yao, J.C., Characterizations of solutions for vector equilibrium problems, J. optim. theory appl., 113, 435-447, (2002) · Zbl 1012.90055
[4] Ansari, Q.H.; Oettli, W.; Schläger, D., A generalization of vectorial equilibria, Math. methods oper. res., 46, 147-152, (1997) · Zbl 0889.90155
[5] Ansari, Q.H.; Siddiqi, A.H.; Wu, S.Y., Existence and duality of generalized vector equilibrium problems, J. math. anal. appl., 259, 115-126, (2001) · Zbl 1018.90041
[6] Ansari, Q.H.; Yang, X.Q.; Yao, J.C., Existence and duality of implicit vector variational problems, Numer. funct. anal. optim., 22, 815-829, (2001) · Zbl 1039.49003
[7] Ansari, Q.H.; Yao, J.C., An existence result for the generalized vector equilibrium problem, Appl. math. lett., 12, 53-56, (1999) · Zbl 1014.49008
[8] Ansari, Q.H.; Yao, J.C., On nondifferentiable and nonconvex vector optimization problems, J. optim. theory appl., 106, 487-500, (2000) · Zbl 0970.90092
[9] Bianchi, M.; Hadjisavvas, N.; Schaible, S., Vector equilibrium problems with generalized monotone bifunctions, J. optim. theory appl., 92, 527-542, (1997) · Zbl 0878.49007
[10] Chen, G.Y.; Craven, B.D., A vector variational inequality and optimization over an efficient set, ZOR-methods models oper. res., 3, 1-12, (1990) · Zbl 0693.90091
[11] Fan, K., A generalization of Tychonoff’s fixed point theorem, Math. ann., 142, 305-310, (1961) · Zbl 0093.36701
[12] Flores-Bazán, F.; Flores-Bazán, F., Vector equilibrium problems under asymptotic analysis, J. global optim., 26, 141-166, (2003) · Zbl 1036.90060
[13] Georgiev, P.G.; Tanaka, T., Vector-valued set-valued variants of Ky Fan’s inequality, J. nonlinear convex anal., 1, 245-254, (2000) · Zbl 0987.49010
[14] ()
[15] Hadjisavvas, N.; Schaible, S., From scalar to vector equilibrium problems in the quasimonotone case, J. optim. theory appl., 96, 297-309, (1998) · Zbl 0903.90141
[16] Komlósi, S., On the Stampacchia and minty variational inequalities, (), 231-260 · Zbl 0989.47055
[17] Konnov, I.V.; Yao, J.C., Existence of solutions for generalized vector equilibrium problems, J. math. anal. appl., 233, 328-335, (1999) · Zbl 0933.49004
[18] G.M. Lee, I.J. Bu, On vector equilibrium problems with multifunctions, Taiwanese J. Math. (2005), in press
[19] Oettli, W., A remark on vector-valued equilibria and generalized monotonicity, Acta math. Vietnam., 22, 213-221, (1997) · Zbl 0914.90235
[20] Oettli, W.; Schläger, D., Generalized vectorial equilibria and generalized monotonicity, (), 145-154 · Zbl 0904.90150
[21] Oettli, W.; Schläger, D., Existence of equilibria for monotone multivalued mappings, Math. methods oper. res., 48, 219-228, (1998) · Zbl 0930.90077
[22] Yuan, G.X.-Z., KKM theory and applications in nonlinear analysis, (1999), Dekker New York
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.