随机增广Lagrange变分不等式的一种求解方法

A solving method for stochastic augmented Lagrange variational inequality

利用变分不等式求解优化问题是一种有效且便利的方法.而随机变分不等式和增广Lagrange变分不等式的概念最近以一种新的形式被阐述,在凸性条件下求解这类问题通常用的方法是逐步对冲算法和分解算法.对于随机优化问题,提出随机增广Lagrange变分不等式.在凸凹鞍点问题中,由随机分解算法求解这类问题.

Variational inequality was an effective and convenient method for solving optimization problems. The concept of a stochastic variational inequality and augmented Lagrange variational inequality has recently been elaborated in a new form. The usual methods for solving these problems were progressive hedging and decomposition algorithms. For stochastic optimization problems stochastic augmented variational inequalities were proposed. In convex and concave saddle point problems stochastic decomposition algorithm was used to solve these problems.