Many important practical problems can be formulated as probabilistic constrained optimization problem (PCOP), which is challenging to solve since it is usually non-convex and non-smooth. Effective methods for (PCOP) mostly focus on approximation techniques. This paper aims at studying the D.C. (difference of two convex functions) approximation techniques. A D.C. approximation is explored to solve the probabilistic constrained optimization problem based on Chen–Harker–Kanzow–Smale (CHKS) smooth plus function. A smooth approximation to probabilistic constraint function is proposed and the corresponding D.C. approximation problem is established. It is proved that the approximation problem is equivalent to the original one under certain conditions. Sequential convex approximation (SCA) algorithm is implemented to solve the D.C. approximation problem. Sample average approximation method is applied to solve the convex subproblem. Numerical results suggest that D.C. approximation technique is effective for optimization with probabilistic constraints.

许多重要的实际问题可以表述为概率约束优化问题（PCOP），该问题很难解决，因为它通常是非凸且非光滑的。 (PCOP) 的有效方法主要集中于近似技术。本文旨在研究DC（两个凸函数之差）逼近技术。探索了 DC 近似来解决基于 Chen–Harker–Kanzow–Smale (CHKS) 平滑加函数的概率约束优化问题。提出了概率约束函数的平滑逼近，并建立了相应的DC逼近问题。证明了在一定条件下该逼近问题与原问题是等价的。序列凸逼近（SCA）算法被实现来解决DC逼近问题。采用样本平均逼近法求解凸子问题。数值结果表明，DC 近似技术对于概率约束的优化是有效的。