摘要
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.
作者
王博
初丽
WANG Bo;CHU Li(College of Mathematics and Statistics,Fuzhou University,Fuzhou,Fujian 350108,China;College of Computer Science and Mathematics,Fujian University of Technology,Fuzhou,Fujian 350118,China)
出处
《福州大学学报（自然科学版）》
CAS
北大核心
2023年第1期13-19,共7页
Journal of Fuzhou University(Natural Science Edition)
基金
国家自然科学青年基金资助项目(11701091)。
关键词
随机优化
互补约束优化
二阶锥
样本平均近似(SAA)
stochastic optimization
optimization with complementarity constraints
second-order cone
sample average approximation(SAA)
