集函数多目标规划的最优性充分条件

Sufficient optimality conditions for multiobjective programming involving n-set functions

在较弱凸性条件下 ,研究了一类可微 n-集函数多目标规划问题的可行解是弱有效解的最优性充分条件。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) ,并给出了 n-折积 An 的子集 S的特征函数〈h,Is〉;其次 ,通过特征函数给出了集函数在子集 S°上可微的定义及集函数在子集 S°上关于第 i个变量 Si 的偏导数定义 ;再次 ,给出了多目标规划问题 ( VP)的弱有效解的概念 ;最后 ,分别在目标函数和约束函数 3种较弱凸性条件下 ,给出了集函数多目标规划问题的可行解是弱有效解的 3个最优性充分条件。

This paper studied a class of multiobjective programing problems involving differentiable n-set functions,and obtained sufficient optimality conditions for weak efficient solutions under generalized convexity conditions.Firstly,we definited pseudometric d(R,S) for n-foldproduct of σ-algebra A of subsets of a given set X,and definite indicator function <h,I s> of subset S of An;Secondly,we gave the concept of differentiable of set function at subset S° and concept of partial derivative at S° with respect to the ith argument S i through in dicator function;Thirdly,we defound the weak efficient solution of (VP);Finally,we obtained three sufficient optimality conditions for weak efficient solutions under generalized convexity conditions.