随机线性互补问题的无约束优化再定式

针对随机线性互补问题,提出等价的无约束优化再定式模型,即由D-间隙函数定义的确定性的无约束期望残差极小化问题.通过拟Monte Carlo方法,将样本进行了推广,得到了相关的离散近似问题.在适当的条件下,提出了最优解存在的充分条件,以及探究了离散近似问题的最优解及稳定点的收敛性.另外,在针对一类带有常系数矩阵的随机互补线性问题,研究了解存在的充要条件.

Unconstrained Optimization Reformulation of Stochastic Linear Complementary Problems

In this paper, the authors present an unconstrained optimization reformulation (UERM problem) forthe stochastic linear complementary problem (SLCP), which is to linebreak minimize an expectedresidual defined by D-gap function. By the quasi-Monte Carlo method, the authors generateobservations and obtain the discrete approximations of the UERM problem.Under some moderate assumptions, the authors establish a sufficient condition for the existenceof solutions to the UERM problem and its discrete approximations. Furthermore,the authors analyze the convergence of optimal solutions and the limiting behaviour ofstationary points of the approximation problems. For a class of SLCPs with a fixedcoefficient matrix, a necessary and sufficient condition for the boundedness ofthe solution sets is discussed as well.