求解随机二阶锥线性互补问题的期望残差最小化方法

ERM method for stochastic linear complementarity problem solution of the second-order cone

引入期望残差最小化(ERM)方法来求解随机二阶锥线性互补问题.在非负象限内,利用ERM方法求解随机线性互补问题是可行的,为此将非负象限内的随机线性互补问题延伸到二阶锥内.首先,介绍了二阶锥矢量相关的若尔当积及谱分解等预备知识.然后,通过二阶锥互补函数FB函数将随机二阶锥线性互补问题转化为极小化问题.以预备知识为基础证明了若尔当积下的x2与x 2的关系,并进一步证明了离散型目标函数解的存在性与收敛性.最后,证明利用ERM方法解随机二阶锥互补问题是可行的.

Expected residual minimization （ERM）method is introduced to solve the stochastic linear complementarity problem of the second-order cone.It has been testified that it is feasible to use ERM method to solve stochastic linear complementarity problem in non-negative quadrant.This method will be extended to the second-order cones.To begin with,some basic knowledge and properties of Jordan algebra and the spectral factorization of vectors associated with the second-order cone are presented. Then,through the second-order cone complementarity function,that is FB function,the stochastic linear complementarity problem of the second-order cone is transformed to be a minimizing problem. The relationship between x 2 and x 2 under the Jordan algebra based on the basic knowledge is proved.Furthermore,the existence and convergence of the solution set of discrete objective function are proved. Finally, a conclusion is drawn that it is feasible to solve the stochastic linear complementarity problem of the second-order cone by using ERM method.