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Super Efficiency for a Vector Equilibrium in Locally Convex Topological Vector Spaces

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Vector Variational Inequalities and Vector Equilibria

Part of the book series: Nonconvex Optimization and Its Applications ((NOIA,volume 38))

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.

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References

  1. 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.

    Article  MATH  Google Scholar 

  2. 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.

    Article  MathSciNet  MATH  Google Scholar 

  3. Borwein J.M. and Zhuang D., “Super Efficiency in Vector Optimiz.”. Transactions of the American Mathem. Soc., Vol. 338, 1993, pp. 105–122.

    Article  MathSciNet  MATH  Google Scholar 

  4. 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.

    Article  MATH  Google Scholar 

  5. 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.

    Google Scholar 

  6. 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.

    MathSciNet  MATH  Google Scholar 

  7. 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.

    Article  MATH  Google Scholar 

  8. 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.

    Article  MATH  Google Scholar 

  9. 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.

    Google Scholar 

  10. Gong X.H., “Efficiency and Henig Efficiency for Vector Variational Inequalities”. Jou. of Optimiz. Theory and Appls.. To appear.

    Google Scholar 

  11. 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.

    Article  MathSciNet  MATH  Google Scholar 

  12. Jahn J., “Mathem. Vector Optimiz. in Partially Ordered Linear Spaces”. Peter Lang, Frankfurt am Main, Germany, 1986.

    Google Scholar 

  13. Jameson G., “Ordered Linear Spaces”. Lecture Notes in Math, Vol. 141, Springer-Verlag. Berlin, 1970.

    Google Scholar 

  14. 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.

    Article  MathSciNet  MATH  Google Scholar 

  15. 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.

    Article  MathSciNet  MATH  Google Scholar 

  16. Robertson A.P. and Robertson W., “Topological Vector Spaces”. Cambridge at the University Press, 1964.

    Google Scholar 

  17. 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.

    Article  MathSciNet  MATH  Google Scholar 

  18. 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.

    Article  MathSciNet  MATH  Google Scholar 

  19. Yang S.Q., “Vector Variational Inequality and its Duality”. Nonlinear Analysis, Theory, Methods and Appls., Vol. 21, 1993, pp. 869–877.

    Article  MATH  Google Scholar 

  20. Yang S.Q., “Vector Variational Inequalities and Vector Pseudolinear Optimiz.”. Jou. of Optimiz. Theory and Appls., Vol. 95, 1997, pp. 729–734.

    Article  MATH  Google Scholar 

  21. Yu S. J. and Yao J.C., “On Vector Variational Inequalities”. Jou. of Optimiz. Theory and Appls., Vol. 89, 1996, pp. 749–769.

    Article  MathSciNet  MATH  Google Scholar 

  22. Zheng X.Y., “Proper Efficiency in Locally Convex Topological Vector Spaces”. Jou. of Optimiz. Theory and Appls., Vol. 94, 1997, pp. 469–486.

    Article  MATH  Google Scholar 

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© 2000 Kluwer Academic Publishers

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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

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  • 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

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