特征函数1_(0,+∞)(z)的一个光滑D.C.近似函数

A smooth D.C.approximation of characteristic function 1_(0,+∞)(z)

基于Pinar-Zenios光滑和函数,提出了特征函数1(0,+∞)(z)的一个光滑D.C.近似函数,讨论了函数的性质,证明了当参数充分小时,光滑函数收敛于特征函数1(0,+∞)(z),并在一定的条件下,建立了概率约束优化问题的一个等价的光滑近似问题.

A smooth D.C.approximation function of characteristic function 10,＋∞）（z）is proposed based on Pinar-Zenios smooth plus function.Some properties of approximation function are discussed.It proves that proposed smooth function converge to characteristic function 1（0,＋∞（z）when the parameter involved is small enough.Under certain conditions,an equivalent smooth approximation problem of chance constrained optimization problem is built.