随机二阶锥互补约束优化模型的一般光滑化SAA方法

A unified SAA framework for stochastic optimization problems with second-order cone complementarity constraints

讨论一般随机二阶锥互补约束问题的求解算法.为处理模型中的不确定性,算法采用样本平均近似(SAA)抽样技术.不同于之前的工作,设计了一般光滑化SAA算法框架,可以在满足要求的一类光滑化函数中根据需要进行选择,从而构造光滑化SAA算法,并保证收敛性.具体的,若SOCMPCC线性无关约束规范等条件成立,则算法构造子问题的稳定点和最优解分别以概率1收敛到原问题的C稳定点和最优解.最后具体给出两个光滑化函数与其对应光滑化SAA算法的例子,由一般光滑化算法框架可得这两种算法收敛.

In this paper,algorithms for a general class of stochastic optimization problem with second-order cone complementarity constraints are investigated.Sample average approximation technique is introduced to handle the uncertainty.This paper suggests a unified smoothing sample average approximation(SAA)framework,which accepts a smoothing function from a broad class to build a convergent smoothing SAA algorithm.It can be proved that if the linear independent constraint qualification for second-order cone constrained optimizations and some other mild assumptions hold,the stationary points and optimal solutions of the generated sub-problem converge to C-stationary points and optimal solutions of second-order cone complementarity constraints with probability one,respectively.In addition,two example smoothing functions and corresponding smoothing SAA algorithms are presented,which can be proved convergent according to the unified smoothing SAA framework.