特征函数$1_{\left(0,+\infty \right)}\left(z\right)$的一类光滑近似函数
A Class of Smooth Approximations of c Haracteristic Function $1_{\left(0,+\infty \right)}\left(z\right)$

特征函数1(0,+∞)(z)在实际中有着广泛的应用，许多重要的实际问题，如概率约束优化问题等都可以转化为与特征函数相关联的问题。然而，特征函数是非连续非光滑的函数，这使得问题的研究较为困难。因此，在实际的研究过程中，寻找特征函数的光滑近似函数显得尤为重要。本文讨论了一类具有特殊性质的特征函数1(0,+∞)(z)的光滑近似函数φ(z,t)，构造了两个具体的光滑近似函数。基于所提出的该类光滑近似函数，给出了概率约束优化问题的等价近似问题。
Characteristic function1(0,+∞)(z)has a wide range of applications in practice, and many important practical problems, such as probabilistic constraint optimization problems, can be transformed into problems associated with characteristic function. However, the characteristic function is a non-continuous and non-smooth function, which makes the study of the problem difficult. Therefore, in the actual research process, it is particularly important to find smooth approximations of characteristic function. In this paper, we discuss a class of smooth approximation functionsφ(z,t)with special properties, and construct two specific smooth approximation functions. Based on the proposed smooth approximation function, the equivalence approximation problem of probabilistic constrained optimization problem is given.