Operations Research Transactions ›› 2020, Vol. 24 ›› Issue (4): 83-92.doi: 10.15960/j.cnki.issn.1007-6093.2020.04.007

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Sensitivity for the second-order S-derivative of the perturbation map in set-valued optimization

TANG Wei1,2,*, YANG Yun3   

  1. 1. Guizhou Radio and TV University, Guiyang 556000, China;
    2. College of Mathematics and Statistics, Guizhou University, Guiyang 550025, China;
    3. Guizhou Vocational and Technical College of ECommerce, Guiyang 550000, China
  • Received:2019-04-01 Published:2020-11-18

Abstract: In this paper, a new kind of second-order contingent derivative is introduced, termed second-order S-derivative. Some properties of second-order S-derivative and the relationship to second-order contingent derivative are discussed. Then, with the help of second-order S-derivative, relationships are established between the minimum of contingent derivative of set-valued maps and contingent derivative of perturbation maps.

Key words: second-order S-derivative, set-valued map, perturbation map

CLC Number: