Acta mathematica scientia,Series B ›› 2002, Vol. 22 ›› Issue (1): 47-55.

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THE OPTIMALITY CONDITIONS OF NONCONVEX SET-VALUED VECTOR OPTIMIZATION

 SHENG Bao-Huai, LIU San-Yang   

  1. Department of Applied Mathematics, Xidian University, Xian 710071, China
  • Online:2002-01-14 Published:2002-01-14
  • Supported by:

    This work is supported by the National Natural Science Foun-dation(69972036) and the Natural Science Foundation of Shanxi province(99SL02)

Abstract:

The concepts of -order Clarke’s derivative, -order Adjacent derivative and -order G.Bouligand derivative of set-valued mappings are introduced, their properties are studied, with which the Fritz John optimality condition of set-valued vector optimization is established. Finally, under the assumption of pseudoconvexity, the optimality condition is proved to be sufficient.

Key words: Set-valued derivative, optimality condition, pseudoconvex set-valued map-ping

CLC Number: 

  • 90C30
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