中文摘要：

研究了一类广义半无限极大极小规划问题,其下层规划的约束集合是一个集值映射。对于这类广义半无限问题,首先利用修正障碍型增广拉格朗日函数将它们在一定条件下转化为标准的半无限极大极小问题,使它们具有相同的局部与全局最优解,从而为这类广义半无限问题提供了可行的解法。给出了实现这种等价转化的两个转化条件：一个是充分与必要条件,另一个是充分条件。与已有文献中的相关转化条件相比,它们均不需要在紧致集上进行转化,而且后一个充分条件在实际中易于验证。最后通过这种转化,给出了这类广义半无限问题的一个新的一阶最优性条件。

英文摘要：

In this paper,we consider a class of generalized semi-infinite min-max problems of the form minx∈Rnψ（x）,where ψ∶Rn→R is defined as ψ（x）=supy∈Z（x）（x,y） and Z（x）={y∈Rm｜f（x,y）≤0,g（y）≤0}.Let Y={y∈Rm｜g（y）≤0},we get ψ（x）=supy∈Y{（x,y）｜f（x,y）≤0}.Firstly, under certain conditions,we use the modified barrier augmented Lagrangian,i.e.,-（x-,y）={{（x,y）-1c∑r1k=1λkφ（cfk（x,y））,y∈Ωc-∞, y∈Y／Ωcwhere x-=（x,λ,c） and Ωc={y∈Y｜cfk（x,y）〈1,k∈r1},to transform（P） into a common semiinfinite min-max problem（P′）.The form of（P′） is min ψ（x）,wher ψ（x）=supФ（x,y）,We give two conditions for the transformation. Condition A is a necessary and sufficient condition, and Condition B is a sufficient condition. Compared with the corresponding conditions in available papers, they do not require the compactness of the constraint Y and Condition B can be verified easily in practice. Then we can obtain the equivalent relation between （P） and （P＇） , i. e. ,if x∈R^n is a local minimizer of （P） with domain of attraction B（x,p） , and Condition A （or Condition B） holds at x, then there exist λ≥0 and ε〉0such that x=（x,λ,ε）is a local minimizer of （ P＇ ） with domain of attraction B（x,p）×R^1×R＋＋; if x=（x,λ,ε）is a local minimizer of （P＇） with domain of attractionB（x,p）×R^1×R＋＋ and Condition A （or Condition B） holds at any x∈R（x,p）,the x∈R^n is a local minimizer of （P） with domain of attraction B（x,p）.Thus we present a feasible approach for solving （P）. Finally, by transformation, we obtain a new first-order optimality condition for （P） under another assumption, i. e. , if x∈R^n is a local minimum of （P） , and Condition A （or Condition B） holds at x, then there exist λ≥0 and ε〉0 such that 0∈Gψ（x）,where x=（x,λ,ε）.