论文标题
最佳控制障碍问题的一阶条件与状态限制
First-order conditions for the optimal control of the obstacle problem with state constraints
论文作者
论文摘要
我们考虑了一个最佳控制问题，其中国家受单方面障碍物问题（从下方出发），并受到点状状态限制（从上方）受到限制。在存在控制约束的情况下，我们通过正规化状态约束证明，C-Stationarity系统对于最优性是必要的。在没有控制限制的情况下，我们表明，通过仔细讨论B型类型的原始一阶条件，局部最小化甚至强烈固定。
We consider an optimal control problem in which the state is governed by an unilateral obstacle problem (with obstacle from below) and restricted by a pointwise state constraint (from above). In the presence of control constraints, we prove, via regularization of the state constraints, that a system of C-stationarity is necessary for optimality. In the absence of control constraints, we show that local minimizers are even strongly stationary by a careful discussion of the primal first-order conditions of B-stationary type.
