概率约束规划问题的一个光滑近似  

A smoothing approximation to chance constrained programs

作　　者：任咏红[1] 张晓有[1] 马燕妮[1] 

机构地区：[1]辽宁师范大学数学学院,辽宁大连116029

出　　处：《辽宁师范大学学报（自然科学版）》2013年第1期7-10,共4页Journal of Liaoning Normal University:Natural Science Edition

基　　金：国家自然科学基金项目(11171138);辽宁省博士科研启动基金项目(20091046)

摘　　要：许多有重要价值的实际问题均属于概率约束问题,该类问题通常是非凸的且非光滑的,有效的求解方法多集中于凸近似方法.基于Sigmoid函数,将概率约束函数光滑化并建立相应的光滑近似问题,通过收敛性分析,证明了在适当的条件下,当参数充分大时,光滑近似问题与原问题等价,且光滑近似问题的最优值和最优解集分别收敛到原问题的最优值和最优解集.Many important practical problems can be formulated as chance constrained programs, which are usually non-convex and non-smooth. Effective methods for chance constrained programs mostly focus on convex approximation techniques. Based on Sigmoid function, this paper proposes a smoothing {unction to approximate the chance constraints and builds the associated smoothed approx- imation problem. The convergence analysis shows that the approximation problem is equivalent to the primal problem when parameter is large enough. In addition, optimal value and the set of optimal so- lutions of the smoothed approximation problem converge to optimal value and the set of optimal solu- tions of chance constrained program under appropriate conditions, respectively.

关 键 词：联合概率约束 SIGMOID函数 光滑近似 收敛性分析 

分 类 号：O221.2[理学—运筹学与控制论]