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Expected Residual Minimization Method for a Class of Stochastic Quasivariational Inequality Problems

机译:一类随机拟变分不等式问题的期望残差最小化方法

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摘要

We consider the expected residual minimization method for a class of stochastic quasivariational inequality problems (SQVIP). The regularized gap function for quasivariational inequality problem (QVIP) is in general not differentiable. We first show that the regularized gap function is differentiable and convex for a class of QVIPs under some suitable conditions. Then, we reformulate SQVIP as a deterministic minimization problem that minimizes the expected residual of the regularized gap function and solve it by sample average approximation (SAA) method. Finally, we investigate the limiting behavior of the optimal solutions and stationary points.
机译:我们考虑了一类随机拟变分不等式问题(SQVIP)的期望残差最小化方法。拟变分不等式问题(QVIP)的正规间隙函数通常是不可微的。我们首先表明,在某些适当条件下,一类QVIP的正则化间隙函数是可微的和凸的。然后,我们将SQVIP重新构造为确定性最小化问题,该问题将正则化间隙函数的期望残差最小化,并通过样本平均逼近(SAA)方法对其进行求解。最后,我们研究了最优解和固定点的极限行为。

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