机会约束优化问题的Log-Sigmoid近似

A Log-Sigmoid approximation to chance constrained programs

许多具有重要价值的实际问题的数学模型均为机会约束优化问题,该类问题通常是非凸且非光滑的,有效求解方法多集中于凸近似.基于Log-Sigmoid函数,将机会约束函数光滑化并且建立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,光滑近似问题的可行集、最优值和最优解集分别收敛于真问题的可行集、最优值和最优解集.

Many important practical problems can be formulated as constrained programs （JCCP） , w hich are usually non-convex and non-smooth .Effective methods for chance constrained programs mostly focus on convex approximation techniques .In this paper ,we propose to smooth the chance constrained programs and establish the associated smoothed Log-Sigmoid approximation problems based on the Log-Sigmoid function .The convergence analysis shows that the feasible set ,the optimal value and the set of optimal solutions of the Log-Sigmoid approximation problem converge to the cor-responding parts of the problem （JCCP） w hen parameter is small enough ,respectively .