具有关联障碍物的单调系统的罚格式：收敛性和误差估计
A penalty scheme for monotone systems with interconnected obstacles: convergence and error estimates
摘要：
针对一类包含单调系统和关联障碍的拟变分不等式，提出了一种新的罚方法。我们表明，对于任何给定的正切换成本，惩罚方程的解决方案单调收敛到那些QVI。我们估计的惩罚误差，并能够推断出，最佳的切换区域的构造准确。我们进一步证明，作为切换成本趋于零，QVI退化到一个方程的HJB型，这是近似的惩罚方程在相同的顺序（直到一个对数因子）的积极的切换成本。最佳切换问题的数值实验验证了理论结果并证明了该方法的有效性。
英文摘要：
We present a novel penalty approach for a class of quasi-variational inequalities (QVIs) involving monotone systems and interconnected obstacles. We show that for any given positive switching cost, the solutions of the penalized equations converge monotonically to those of the QVIs. We estimate the penalization errors and are able to deduce that the optimal switching regions are constructed exactly. We further demonstrate that as the switching cost tends to zero, the QVI degenerates into an equation of HJB type, which is approximated by the penalized equation at the same order (up to a log factor) as that for positive switching cost. Numerical experiments on optimal switching problems are presented to illustrate the theoretical results and to demonstrate the effectiveness of the method.
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