Abstract
This paper deals with the vector equilibrium problem. The concept of super efficiency for vector equilibrium is introduced. A scalar characterization of super efficient solution for vector equilibrium is given. By using of the scalarization result, we discuss the connectedness of super efficient solutions set to the vector equilibrium problems in locally convex topological vector spaces.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Ansari Q.H., Oettli W. and Schiäger D., “A Generalization of Vectorial Equilibria”. Mathem. Methods of Operations Research, Vol. 46, No. 2, 1997, pp. 147–152.
Bianchi M., Hadjisavvas N. and Schaible S., “Vector Equilibrium Problems with Generalized Monotone Bifunctions”. Jou. of Optimiz. Theory and Appls., Vol. 92, 1997, pp. 527–542.
Borwein J.M. and Zhuang D., “Super Efficiency in Vector Optimiz.”. Transactions of the American Mathem. Soc., Vol. 338, 1993, pp. 105–122.
Chen G.-Y., “Existence of Solutions for a Vector Variational Inequality: A Extension of the Hartman-Stampacchia Theorem”. Jou. of Optimiz. Theory and Appls., Vol. 74, 1992, pp. 445–456.
Chen G.-Y. and Cheng G.M., “Vector Variational Inequalities and Vector Optimiz.”. Lecture Notes in Econ. and Mathem. Systems, Springer-Verlag, Heideberg, Germany, Vol. 258, 1987, pp. 408–416.
Chen G.-Y. and Craven B.D., “A Vector Variational Inequality and Optimiz. over the Efficient Set”. Zeitschrift für Operations Research, Vol. 34, 1990, pp. 1–12.
Chen G.-Y. and Li S.J., “Existence of Solutions for a Generalized Vector Quasi-variational Inequality”, Jou. of Optimiz. Theory and Appls., Vol. 90, 1996, pp. 321–334.
Chen G.-Y. and Yang S.Q., “Vector Complementarity Problem and its Equivalences with the Weak Minimal Element in Ordered Spaces”. Jou. of Mathem. Analysis and Appls., Vol. 153, 1990, pp. 136–158.
Giannessi F., “Theorems of the Alternative, Quadratic Programs and Complementarity Problems”. In “Variational Inequalities and Complementarity Problems”, Edited by R. W. Cottle, F. Giannessi and J.-L. Lions, J. Wiley and Sons, New York, New York, 1980, pp. 151–186.
Gong X.H., “Efficiency and Henig Efficiency for Vector Variational Inequalities”. Jou. of Optimiz. Theory and Appls.. To appear.
Gwinner J. and Oettli W., “Theorems of the Alternative and Duality for Inf-sup Problems”. Mathematics of Operations Research, Vol. 19, 1994, pp. 238–256.
Jahn J., “Mathem. Vector Optimiz. in Partially Ordered Linear Spaces”. Peter Lang, Frankfurt am Main, Germany, 1986.
Jameson G., “Ordered Linear Spaces”. Lecture Notes in Math, Vol. 141, Springer-Verlag. Berlin, 1970.
Lee K.L., Lee B.S. and Chang S.S., “On Vector Quasivariational Inequalities”. Jou. of Mathem. Analysis and Appls., Vol. 203, 1996, pp. 626–638.
Lin K.L., Yang D.P. and Yao J.C., “Generalized Vector Variational Inequalities”. Jou. of Optimiz. Theory and Appls., Vol. 92, 1997, pp. 117–125.
Robertson A.P. and Robertson W., “Topological Vector Spaces”. Cambridge at the University Press, 1964.
Siddiqi A.H., Ansari Q.H. and Khaliq A., “On Vector Variational Inequalities”. Jou. of Optimiz. Theory and Appls., Vol. 84, 1995, pp. 171–180.
Warburton A.R., “Quasiconcave Vector Maximization: Connectedness of the Sets of Pareto-Optimal and Weak Pareto-Optimal Alternatives”. Jou. of Optimiz. Theory and Appls., Vol. 40. 1983, pp. 537–557.
Yang S.Q., “Vector Variational Inequality and its Duality”. Nonlinear Analysis, Theory, Methods and Appls., Vol. 21, 1993, pp. 869–877.
Yang S.Q., “Vector Variational Inequalities and Vector Pseudolinear Optimiz.”. Jou. of Optimiz. Theory and Appls., Vol. 95, 1997, pp. 729–734.
Yu S. J. and Yao J.C., “On Vector Variational Inequalities”. Jou. of Optimiz. Theory and Appls., Vol. 89, 1996, pp. 749–769.
Zheng X.Y., “Proper Efficiency in Locally Convex Topological Vector Spaces”. Jou. of Optimiz. Theory and Appls., Vol. 94, 1997, pp. 469–486.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Kluwer Academic Publishers
About this chapter
Cite this chapter
Gong, X.H., Fu, W.T., Liu, W. (2000). Super Efficiency for a Vector Equilibrium in Locally Convex Topological Vector Spaces. In: Giannessi, F. (eds) Vector Variational Inequalities and Vector Equilibria. Nonconvex Optimization and Its Applications, vol 38. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0299-5_13
Download citation
DOI: https://doi.org/10.1007/978-1-4613-0299-5_13
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-7985-0
Online ISBN: 978-1-4613-0299-5
eBook Packages: Springer Book Archive