SIAM Journal on Control and Optimization, Volume 58, Issue 6, Page 3508-3532, January 2020.
For a class of quasi-variational inequalities (QVIs) of obstacle type the stability of its solution set and associated optimal control problems are considered. These optimal control problems are nonstandard in the sense that they involve an objective with set-valued arguments. The approach to study the solution stability is based on perturbations of minimal and maximal elements of the solution set of the QVI with respect to monotone perturbations of the forcing term. It is shown that different assumptions are required for studying decreasing and increasing perturbations and that the optimization problem of interest is well-posed.

中文翻译：

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拟变分不等式解集的稳定性和最优控制

SIAM控制与优化杂志，第58卷，第6期，第3508-3532页，2020年1月。
对于一类障碍类型的拟变分不等式（QVI），需要考虑其解集的稳定性以及相关的最优控制问题。这些最佳控制问题在某种意义上是非标准的，因为它们涉及带有设定值参数的目标。研究解稳定性的方法是基于QVI解集的最小和最大元素对强迫项的单调摄动的摄动。结果表明，研究减少和增加的扰动需要不同的假设，并且所关注的优化问题是恰当的。