| 吴学谦,李声杰.随机线性互补问题的无约束优化再定式[J].数学年刊A辑,2019,(1):043~54 |
| 随机线性互补问题的无约束优化再定式 |
| Unconstrained Optimization Reformulation of Stochastic Linear Complementary Problems |
| Received:March 29, 2017 Revised:April 14, 2018 |
| DOI：10.16205/j.cnki.cama.2019.0005 |
| 中文关键词: Stochastic linear complementary problem, UERM problem, Quasi-Monte Carlo method |
| 英文关键词:Stochastic linear complementary problem, UERM problem, Quasi-Monte Carlo method |
| 基金项目: |
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| 中文摘要: |
| 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. |
| 英文摘要: |
| In this paper, the authors present an unconstrained optimization reformulation (UERM problem) for
the stochastic linear complementary problem (SLCP), which is to \linebreak minimize an expected
residual defined by D-gap function. By the quasi-Monte Carlo method, the authors generate
observations and obtain the discrete approximations of the UERM problem.
Under some moderate assumptions, the authors establish a sufficient condition for the existence
of solutions to the UERM problem and its discrete approximations. Furthermore,
the authors analyze the convergence of optimal solutions and the limiting behaviour of
stationary points of the approximation problems. For a class of SLCPs with a fixed
coefficient matrix, a necessary and sufficient condition for the boundedness of
the solution sets is discussed as well. |
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