Stability of the Solution Set of Quasi-variational Inequalities and Optimal Control
Stability of the Solution Set of Quasi-variational Inequalities and Optimal Control
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DOI：
10.1137/19m1250327
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发表时间：
2019-04
期刊：
影响因子：
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通讯作者：
A. Alphonse;M. Hintermüller;C. N. Rautenberg
中科院分区：
文献类型：
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作者：
A. Alphonse;M. Hintermüller;C. N. Rautenberg
研究了一类障碍型拟变分不等式解集的稳定性及其最优控制问题。这些最优控制问题是非标准的，因为它们涉及一个具有集值参数的目标。研究解的稳定性的方法是基于最小和最大元素对QVI的解集的扰动相对于单调扰动的强迫项。研究表明，研究减少和增加的扰动需要不同的假设，并且感兴趣的优化问题是适定的。
For a class of quasivariational inequalities (QVIs) of obstacle-type the stability of its solution set and associated optimal control problems are considered. These optimal control problems are non-standard 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 to the solution set of the QVI with respect to monotonic 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.