Stochastic Approximation Approaches to the Stochastic Variational Inequality Problem

Houyuan Jiang; Huifu Xu

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Stochastic Approximation Approaches to the Stochastic Variational Inequality Problem

机译：随机变分不等式问题的随机逼近方法

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Stochastic approximation methods have been extensively studied in the literature for solving systems of stochastic equations and stochastic optimization problems where function values and first order derivatives are not observable but can be approximated through simulation. In this paper, we investigate stochastic approximation methods for solving stochastic variational inequality problems (SVIP) where the underlying functions are the expected value of stochastic functions. Two types of methods are proposed: stochastic approximation methods based on projections and stochastic approximation methods based on reformulations of SVIP. Global convergence results of the proposed methods are obtained under appropriate conditions.

机译：随机逼近方法已在文献中得到广泛研究，用于解决随机方程组和随机优化问题，其中函数值和一阶导数不可观察，但可以通过仿真近似。在本文中，我们研究用于解决随机变分不等式问题（SVIP）的随机逼近方法，其中基础函数是随机函数的期望值。提出了两种类型的方法：基于投影的随机逼近方法和基于SVIP公式的随机逼近方法。在适当的条件下获得了所提出方法的全局收敛结果。

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《IEEE Transactions on Automatic Control》 |2008年第6期|p.1462-1475|共14页
作者
Houyuan Jiang; Huifu Xu;
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正文语种 eng
中图分类自动化系统;
关键词
approximation theory; stochastic processes; variational techniques; first order derivatives; stochastic approximation approach; stochastic equations; stochastic optimization problem; stochastic variational inequality problem; Projection method; simulation; stochas;

机译：逼近理论;随机过程;变分技术;一阶导数;随机逼近方法;随机方程;随机优化问题;随机变分不等式问题;投影方法;仿真;随机;

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8. I,II Convergence and Rate of Convergence Theorems for Constrained and Unconstrained Stochastic Approximation,via Weak Convergence Methods. III Numerical Studies for Constrained Stochastic Approximation Problems, [R] . kushner,harold j. lakshmivarahan, s. 1977

机译：I，II收敛性和受约束和无约束随机逼近的收敛速度定理，通过弱收敛方法。 III约束随机逼近问题的数值研究，

Stochastic Approximation Approaches to the Stochastic Variational Inequality Problem

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