集值映射多目标规划的K-T最优性条件

K-T TYPE OPTIMALITY CONDITIONS OF MULTIOBJECTIVE PROGRAMMING WITH SET-VALUED MAPS

讨论集值映射多目标规划（ＶＰ）的最优性条件问题．首先，在没有锥凹的假设下， 利用集值映射的相依导数，得到了（ＶＰ）的锥－超有效解要满足的必要条件和充分条件． 其次，在锥凹假设和比推广了的 Ｓｌａｔｅｒ规格更弱的条件下，给出了（ＶＰ）关于锥－超有效 解的Ｋ－Ｔ型最优性必要条件和充分条件．

in this paper , we discuss the optimality condition problems of multiobjective programming (VP) with set-valued maps. First, without cone concave assumption, some necessary and sufficient optimality conditions for cone-super efficient solution of (VP) are given by using the contingent derivative of the set-valued maps. Secondly, under cone concave assumption and condition which is weaker than the generalized Slater constraint qualification, we give K-T type necessary and sufficient optimality conditions for cone-super efficient solution of (VP).