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Existence of Solutions and Variational Principles for Generalized Vector Systems

Author

Listed:
  • L. C. Ceng

    (Shanghai Normal University)

  • G. Mastroeni

    (University of Pisa, Largo B. Pontecorvo 5)

  • J. C. Yao

    (National Sun Yat-Sen University)

Abstract

By means of generalized KKM theory, we prove a result on the existence of solutions and we establish general variational principles, that is, vector optimization formulations of set-valued maps for vector generalized systems. A perturbation function is involved in general variational principles. We extend the theory of gap functions for vector variational inequalities to vector generalized systems and we prove that the solution sets of the related vector optimization problems of set-valued maps contain the solution sets of vector generalized systems. A further vector optimization problem is defined in such a way that its solution set coincides with the solution set of a weak vector generalized system.

Suggested Citation

  • L. C. Ceng & G. Mastroeni & J. C. Yao, 2008. "Existence of Solutions and Variational Principles for Generalized Vector Systems," Journal of Optimization Theory and Applications, Springer, vol. 137(3), pages 485-495, June.
    • Handle: RePEc:spr:joptap:v:137:y:2008:i:3:d:10.1007_s10957-007-9348-0
    DOI: 10.1007/s10957-007-9348-0
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    References listed on IDEAS

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    1. Q. H. Ansari & I. V. Konnov & J. C. Yao, 2001. "Existence of a Solution and Variational Principles for Vector Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 110(3), pages 481-492, September.
    2. M. Bianchi & N. Hadjisavvas & S. Schaible, 1997. "Vector Equilibrium Problems with Generalized Monotone Bifunctions," Journal of Optimization Theory and Applications, Springer, vol. 92(3), pages 527-542, March.
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