联合概率约束问题的一个光滑函数法

许多有重要价值的实际问题均属于联合概率约束优化问题（JCCP），该类问题通常是非凸的并且非光滑，有效求解方法多集中于凸近似方法，往往局限于具有单个概率约束的问题．本文基于两个凸函数之差（即D．C．函数）为约束的近似优化问题，提出了约束函数的光滑近似函数以及相应的光滑近似问题．通过收敛性分析，证明了当参数充分小时，光滑化的近似问题的最优值和最优解集分别收敛到（JCCP）的最优值和最优解集．

A Smoothing Function Approach to Joint Chance Constrained Programs

Many important practical problems can be formulated as joint chance constrained programs （JCCP）, which are usually non-convex and non-smooth. Effective methods for joint chance constrained programs mostly focus on con- vex approximation techniques. Moreover, chance constrained program is often confined to the one with a single probabilit- ic constraint. This paper proposes a smoothing function for approximate optimization problems with constraints based on the difference of two convex functions （i.e.D.C. function）, and the associated smoothed approximation problems. The convergence analysis shows that optimal value and the set of optimal solutions of the smoothed approximate problem con- verge to optimal value and the set of optimal solutions of （JCCP） when parameter is small enough, respectively.