A Smoothing Function Approach to Joint Chance-Constrained Programs
A Smoothing Function Approach to Joint Chance-Constrained Programs
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DOI：
10.1007/s10957-013-0513-3
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发表时间：
2014-01
影响因子：
1.9
通讯作者：
F. Shan;Liwei Zhang;X. Xiao
中科院分区：
文献类型：
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作者：
F. Shan;Liwei Zhang;X. Xiao
在这篇文章中，我们考虑了DC（两个凸函数的差异）函数方法求解联合机会约束规划（JCCP），这是由Hong等人首先建立的。（Oper Res 59：617 - 630，2011）。他们使用DC函数来逼近概率函数，并构造了一种序贯凸逼近方法来解决逼近问题。然而，他们使用的DC函数是不可微的。为了缓解这一困难，我们提出了一类光滑函数来近似联合机会约束函数，基于此构造光滑优化问题来近似JCCP。我们证明了光滑逼近序列的解在一定的渐近条件下收敛于JCCP的Karush-Kuhn-Tucker点。为了实现所提出的方法，四个例子中的类平滑函数进行了探讨。此外，数值实验表明，我们的方法是可比的和有效的。
In this article, we consider a DC (difference of two convex functions) function approach for solving joint chance-constrained programs (JCCP), which was first established by Hong et al. (Oper Res 59:617–630, 2011). They used a DC function to approximate the probability function and constructed a sequential convex approximation method to solve the approximation problem. However, the DC function they used was nondifferentiable. To alleviate this difficulty, we propose a class of smoothing functions to approximate the joint chance-constraint function, based on which smooth optimization problems are constructed to approximate JCCP. We show that the solutions of a sequence of smoothing approximations converge to a Karush–Kuhn–Tucker point of JCCP under a certain asymptotic regime. To implement the proposed method, four examples in the class of smoothing functions are explored. Moreover, the numerical experiments show that our method is comparable and effective.