Abstract
In this paper, the concept of a vector semi-monotone operator is introduced. This concept is applied to establish several existence results of vector variational inequalities. These extend some results of others.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
F.E. Browder (1968) ArticleTitleSemi-contract and semi-accretive nonlinear mappings in Banach space Bulletin of American Mathematics Society 74 660–665
S.S. Chang (2000) ArticleTitleSet-valued variational inclusions in Banach spaces Journal of Mathematical Analysis and Applications 248 438–454 Occurrence Handle10.1006/jmaa.2000.6919
G.Y. Chen (1992) ArticleTitleExistence of solutions for a vector variational inequality: an extention of the Hartman–Stampacchia theorem Journal of Optimization Theory and Applications 74 445–455 Occurrence Handle10.1007/BF00940320
Y.Q. Chen (1999) ArticleTitleOn the semi-monotone operator theory and applications Journal of Mathematical Analysis and Applications 231 177–192 Occurrence Handle10.1006/jmaa.1998.6245
G.Y. Chen X.Q. Yang (1990) ArticleTitleThe vector complementarity problem and its equivalence with the weak minimal elements in ordered spaces Journal of Mathematical Analysis and Applications 153 136–158 Occurrence Handle10.1016/0022-247X(90)90223-3
F. Giannessi (1980) Theorems of alternative, quadratic programs and complementary problems R.W. Cottle F. Giannessi J.L. Lions (Eds) Variatonal Inequalities and Complementarity Problems. Wiley New-York 151–186
I.V. Konnov J.C. Yao (1997) ArticleTitleOn the generalized vector variational inequality problem Journal of Mathematical Analysis and Applications 206 42–58 Occurrence Handle10.1006/jmaa.1997.5192
K.L. Lin D.P. Yang J.C. Yao (1997) ArticleTitleGeneralized vector variational inequalities Journal of Optimization Theory and Applications. 92 117–125 Occurrence Handle10.1023/A:1022640130410
X.Q. Yang (1993) ArticleTitleVector variational inequality and its duality Nonlinear Analysis 21 869–877 Occurrence Handle10.1016/0362-546X(93)90052-T
S.J. Yu J.C. Yao (1997) ArticleTitleOn vector variational inequalities Journal of Optimization Theory and Applications 89 749–769
E. Zeidle (1988) Nonlinear functional analysis and its applications, Vol. 4 Springer-Verlag Berlin, New York
Author information
Authors and Affiliations
Corresponding author
Additional information
The work is supported by the Natural Science Foundation of China (Grant No. 19671042) and the Doctoral Program Foundation of the Ministry of Education of China.
Rights and permissions
About this article
Cite this article
Zheng, F. Vector Variational Inequalities with Semi-monotone Operators. J Glob Optim 32, 633–642 (2005). https://doi.org/10.1007/s10898-004-2698-3
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s10898-004-2698-3