求解随机广义垂直线性互补问题的随机近似方法
Stochastic Approximation Approaches to Stochastic Extended Vertical Complementarity Problem
摘要: 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。
Abstract: 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.
文章引用：杨妍娇, 王奕菲, 张杰. 求解随机广义垂直线性互补问题的随机近似方法[J]. 应用数学进展, 2023, 12(4): 1467-1473. https://doi.org/10.12677/AAM.2023.124151

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