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Sharp Efficiency for Vector Equilibrium Problems on Banach Spaces

Author

Listed:
  • Si-Huan Li
  • Qiang Wang
  • Shu Xu
  • Jun-Xiang Wang

Abstract

The concept of sharp efficient solution for vector equilibrium problems on Banach spaces is proposed. Moreover, the Fermat rules for local efficient solutions of vector equilibrium problems are extended to the sharp efficient solutions by means of the Clarke generalized differentiation and the normal cone. As applications, some necessary optimality conditions and sufficient optimality conditions for local sharp efficient solutions of a vector optimization problem with an abstract constraint and a vector variational inequality are obtained, respectively.

Suggested Citation

  • Si-Huan Li & Qiang Wang & Shu Xu & Jun-Xiang Wang, 2013. "Sharp Efficiency for Vector Equilibrium Problems on Banach Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:128178
    DOI: 10.1155/2013/128178
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    References listed on IDEAS

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    2. N. Hadjisavvas & S. Schaible, 1998. "From Scalar to Vector Equilibrium Problems in the Quasimonotone Case," Journal of Optimization Theory and Applications, Springer, vol. 96(2), pages 297-309, February.
    3. 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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