基于蒙特卡洛方法求解随机变分不等式
摘要
采取外梯度方法结合随机逼近方法求解随机变分不等式.考虑在每次迭代时取一个样本点并且结合线搜索使得计算率大大提高,最后在适当的假设下证明了算法的全局收敛性,初步的数值实验表明该算法是有效的.
引文
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[2]Kushner H,Yin G G.Stochastic Approximation and Recursive Algorithms and Applications[M].New York:Springer,2003.
[3]Spall J C.Introduction to Stochastic Search and Optimization:Estimation,Simulation,and Control[M].New York:John Wiley and Sons,2005.
[4]Iusem A N,JofréA,Oliveira R I,et al.Extragradient method with variance reduction for stochastic variational inequalities[J].SIAM Journal on Optimization,2017,27(2):686-724.
[5]Iusem A N,JofréA,Oliveira R I,et al.VarianceBased extragradient methods with line Search for stochastic variational inequalities[J].SIAM Journal on Optimization,2019,29(1):175-206.
[6]Facchinei F,Pang J S.Finite-Dimensional Variational Inequalities and Complementarity Problems[M].New York:Springer,2003.
[7]H Robbins,D Siegmund.A convergence theorem for nonnegative almost supermartingales and some applications,in Optimizing Methods in Statistics[M].New York:J.S.Rustagi,eds, Academic Press,1971:233–257..
[8]Wang M Z,Lin G H,Gao Y L,et al.Sample average approximation method for a class of stochastic variational inequality problems[J].Journal of Systems Science and Complexity,2011,24(6):1143-1153.