一类广义半无限规划问题的一阶最优性条件

摘要

In this paper, a kind of generalized semi-infinite min-max programming problem is transformed into a common semi-infinite min-max programming problem by utilizing a exact augmented Lagrange function. The relations of optimal solutions and optimal values between generalized semi-infinite min-max programming problem and common semi-infinite min-max programming problem are discussed. According to these relations and the first-order optimality condition of common semi-infinite min-max programming problem, the first-order optimality condition of this kind of generalized senti-infinite min-max programming problem is presented.%本文利用一个精确增广Lagrange函数研究了一类广义半无限极小极大规划问题.在一定的条件下将其转化为标准的半无限极小极大规划问题.研究了这两类问题的最优解和最优值之间的关系,利用这种关系和标准半无限极小极大规划问题的一阶最优性条件给出了这类广义半无限极小极大规划问题的一个新的一阶最优性条件.