Acta mathematica scientia,Series A ›› 2012, Vol. 32 ›› Issue (4): 685-690.

• Articles • Previous Articles     Next Articles

Generalized Gradient of Set-valued Optimization Problems and Optimality Conditions of Strong-efficient Solutions

 YU Li, XU Xi-Hong   

  1. 1.Department of Mathematics, Nanchang University, Nanchang 330031|2.Institute of Mathematics and Computer of Science, Yichun University, Jiangxi Yichun 336000
  • Received:2010-08-12 Revised:2011-09-29 Online:2012-08-25 Published:2012-08-25
  • Supported by:

    国家自然科学基金(10461007)和江西省自然科学基金(2009GZS0021)资助

Abstract:

A kind of generalized gradient for set-valued map is introduced in ordered Banach spaces. Under the connected condition, its existence is proved by the separation theorem for convex sets. As an application, the optimality necessary and sufficient conditions of strong-efficient solution for set-valued optimization problem are established in terms of the generalized gradient.

Key words: Set-valued optimization, Contingent derivative,  Strong-efficiency, Generalized gradient, Optimality condition

CLC Number: 

  • 90C28
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