Abstract
This paper deals with generalized vector quasi-equilibrium problems. By virtue of a nonlinear scalarization function, the gap functions for two classes of generalized vector quasi-equilibrium problems are obtained. Then, from an existence theorem for a generalized quasi-equilibrium problem and a minimax inequality, existence theorems for two classes of generalized vector quasi-equilibrium problems are established.
Similar content being viewed by others
References
Q.H. Ansari Fabian Flores-Bazan (2003) ArticleTitleGeneralized vector quasi-equilibrium problems with applications Journal of Mathematical Analysis and Applications 277 246–256 Occurrence Handle10.1016/S0022-247X(02)00535-8
J.P. Aubin I. Ekeland (1984) Applied Nonlinear Analysis John Wiley and Sons New York
G.Y. Chen C.J. Goh X.Q. Yang (1999) ArticleTitleVector network equilibrium problems and nonlinear scalarization methods Mathematical Methods of Operation Research 49 239–253
G.Y. Chen C.J. Goh X.Q. Yang (2000) On gap functions for vector variational inequalities F. Giannessi (Eds) Vector Variational Inequalities and Vector Equilibria Kluwer Academic Publishers Dordrecht, Holland 55–72
Chen, G.Y., Yang, X.Q. and Yu, H. (2004), A nonlinear scalarization function and generalized quasi-vector equilibrium problems, Journal of Global Optimization. In press, available online.
C. Gerth P. Weidner (1990) ArticleTitleNonconvex separation theorems and some applications in vector optimization Journal of Optimization Theory and Applications 67 297–320 Occurrence Handle10.1007/BF00940478
C.W. Ha (1980) ArticleTitleMinimax and fixed point theorems Mathematische Annalen 248 73–77 Occurrence Handle10.1007/BF01349255
I.V. Konnov J.C. Yao (1999) ArticleTitleExistence of solutions for generalized vector equilibrium problems Journal of Mathematical Analysis and Applications 233 328–335 Occurrence Handle10.1006/jmaa.1999.6312
D. Kuroiwa (1996) ArticleTitleConvexity for set-valued maps Applied Mathematics Letter 9 97–101
S.J. Li K.L. Teo X.Q. Yang (2005) ArticleTitleGeneralized vector quasi-equilibrium problems Mathematical Methods of Operations Research 61 3
Li, S.J., Teo, K.L. and Yang, X.Q., On generalized vector quasi-equilibrium problems,preprint.
S.J. Li H. Yan G.Y. Chen (2003) ArticleTitleDifferential and sensitivity properties of gap functions for vector variational inequalities Mathematical Methods of Operations Research 57 377–391
X.Q. Yang (2003) ArticleTitleOn the gap functions of prevariational inequalities Journal of Optimization Theory and Applications 116 437–452 Occurrence Handle10.1023/A:1022422407705
X.Q. Yang J.C. Yao (2002) ArticleTitleGap functions and existence of solutions to set-valued vector variational inequalities Journal of Optimization Theory and Applications 115 407–417 Occurrence Handle10.1023/A:1020844423345
Author information
Authors and Affiliations
Corresponding author
Additional information
This research is partially supported by the Postdoctoral Fellowship Scheme of The Hong Kong Polytechnic University and the National Natural Science Foundation of China.
Rights and permissions
About this article
Cite this article
Li, S.J., Teo, K.L., Yang, X.Q. et al. Gap Functions and Existence of Solutions to Generalized Vector Quasi-Equilibrium Problems. J Glob Optim 34, 427–440 (2006). https://doi.org/10.1007/s10898-005-2193-5
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s10898-005-2193-5