求解随机向量变分不等式的样本平均逼近方法

Sample Average Approximation Method for Stochastic Vector Variational Inequalities

研究了随机向量变分不等式的期望值模型。通过借助于标量化方法以及正则化间隙函数将随机向量变分不等式转化为随机优化问题。由于优化问题的目标函数中含有数学期望,故提出了求解该问题的样本平均逼近方法。在适当的假设条件下,证明了样本平均逼近问题最优值和最优解的收敛性。所得结果为研究随机向量变分不等式提供了新方法。

Studies the Expected value model of stochastic vector variational inequalities problems.By using the scalar method and regularized gap function transform stochastic vector variational inequalities to stochastic optimization problem.we propose a sample average approximation method for solving the expected value model.Under appropriate assumptions,the convergence of the optimal solution of the sample average approximation problem are proved.The results provide a new idea for the study of Stochastic Vector Variational Inequalities.