n-集函数多目标规划的对偶

Duality for multiobjective programming involving n-set functions

在较弱凸性条件下,研究了一类可微n集函数的多目标规划问题的对偶问题。首先,对已知集X的子集的σ代数A的n折积An,定义了伪度量d(R,S),给出了相应的特征函数〈h,Is〉;其次,通过特征函数给出了集函数在S°可微的定义及集函数在S°关于第i个变量Si的偏导数定义;给出了多目标规划问题(VP)的弱有效解概念及(VP)的最优性必要条件;最后,分别在目标函数和约束函数的3种较弱凸性条件下,研究n集函数多目标规划问题的对偶问题,获得了3个弱对偶结果和强对偶结果。

This paper studied duality problems of a class of multiobjective programming involving differentiable n-set functions under generalized convexity conditions. Firstly, this paper definited pseudometric d（R,S） for n -foldproduct of σ-algebra A of subsets of a given set X , and definited indicator function （h,Is） ; secondly, gave the concept of differentiable of set function at S° and concept of partial derivative at S° with respect to the ith argument Si through indicator function, and defound the weak efficient solution of （VP） and optimality necessary condition; Finally, obtained three weak duality results and strong duality results under generalized convexity conditions. 8 refs.