论文标题
强大的平稳性条件，用于由速率独立的进化变化不等式控制的最佳控制问题
Strong Stationarity Conditions for Optimal Control Problems Governed by a Rate-Independent Evolution Variational Inequality
论文作者
论文摘要
我们证明了最佳控制问题的强烈平稳性条件，这些条件受原型与速率非依赖性进化变化不平等的影响，即以原始偶型乘数系统形式的一阶必要最优化条件，等同于纯粹的bouligand startarity的原始概念。我们的分析依赖于标量停止操作员的Hadamard定向可不同性的最新结果，以及一个新的暂时性多面体概念，该概念概括了Mignot的经典思想。将建立的强固定系统与已知的最佳控制问题进行了比较，该条件是由椭圆障碍型的变化不平等和平稳性系统控制的最佳控制问题。
We prove strong stationarity conditions for optimal control problems that are governed by a prototypical rate-independent evolution variational inequality, i.e., first-order necessary optimality conditions in the form of a primal-dual multiplier system that are equivalent to the purely primal notion of Bouligand stationarity. Our analysis relies on recent results on the Hadamard directional differentiability of the scalar stop operator and a new concept of temporal polyhedricity that generalizes classical ideas of Mignot. The established strong stationarity system is compared with known optimality conditions for optimal control problems governed by elliptic obstacle-type variational inequalities and stationarity systems obtained by regularization.
