论文标题
在Banach空间中具有几乎确定状态限制的Banach空间中凸的随机优化问题的最佳条件
Optimality Conditions for Convex Stochastic Optimization Problems in Banach Spaces with Almost Sure State Constraints
论文作者
论文摘要
我们分析了一个凸随机优化问题，其中认为状态属于基本界限随机变量的Bochner空间，其中图像在反射性和可分开的Banach空间中。对于这个问题，我们获得了必要和足够的模型的最佳条件。此外，与最佳条件相关的Lagrange乘数是可集成的矢量值函数，而不仅仅是衡量措施。给出了模型问题，以证明在不确定性下对PDE受限优化的应用，并具有进一步应用的前景。
We analyze a convex stochastic optimization problem where the state is assumed to belong to the Bochner space of essentially bounded random variables with images in a reflexive and separable Banach space. For this problem, we obtain optimality conditions that are, with an appropriate model, necessary and sufficient. Additionally, the Lagrange multipliers associated with optimality conditions are integrable vector-valued functions and not only measures. A model problem is given demonstrating the application to PDE-constrained optimization under uncertainty with an outlook for further applications.
