%0 Journal Article
%T 求解随机广义垂直线性互补问题的随机近似方法<br>Stochastic Approximation Approaches to Stochastic Extended Vertical Complementarity Problem
%A 杨妍娇
%A 王奕菲
%A 张杰
%J Advances in Applied Mathematics
%P 1467-1473
%@ 2324-8009
%D 2023
%I Hans Publishing
%R 10.12677/AAM.2023.124151
%X 近几年随机广义垂直线性互补问题的求解方法不断完善。本文提出了一种新型的求解随机广义垂直线性互补问题(SEVLCP)的方法，即随机近似(SA)算法。基于Fischer-Burmeister函数的性质，先将随机广义垂直线性互补问题转化为无约束极小化问题，再利用随机近似算法进行求解。本文详细讨论了原问题的重新构造过程，并提出了一种有效求解的迭代格式，以及在适当的条件下，得到了所提出方法的全局收敛结果。<br />
In recent years, the solution methods of stochastic extended vertical linear complementarity prob-lems have been continuously improved. In this paper, a new method for solving stochastic extended vertical linear complementarity problem (SEVLCP) is proposed, namely stochastic approximation (SA) methods. Based on the properties of the Fischer-Burmeister function, the stochastic extended vertical linear complementarity problem is reformulated in terms of the unconstrained minimiza-tion problem, and then solved by the stochastic approximation methods. This paper discusses the reformulation process of the original problem in detail, and proposes an iterative scheme for effec-tive solving, and obtains the global convergence results of the proposed method under appropriate conditions.
%K 随机广义垂直线性互补问题，随机近似方法，Fischer-Burmeister函数<br>Stochastic Extended Vertical Linear Complementarity Problem
%K Stochastic Approximation 
Approaches
%K Fischer-Burmeister Function
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=63833