Chance constraints with feedback and integrality (B04)

这个项目的目标是将概率或机会约束纳入天然气管网优化模型。这使得人们能够在存在不确定参数（如气体负荷）的情况下做出风险规避的最优决策。主要应用是具有层次结构的模型（例如，双层天然气市场模型）或具有静态或瞬态气流的模型。这些嵌入结构导致了新的挑战，在理论分析（例如，可微性，凸性，存在的解决方案），以及在算法解决方案（例如，相对于无限随机不等式系统的概率约束）。该项目研究的一个主要方面是从静态到动态的机会约束的过渡。

The goal of this project is to incorporate probabilistic or chance constraints into models of gas network optimization. This allows one to take risk averse optimal decisions in the presence of uncertain parameters such as gas load. Main applications are models with hierarchical structure (e.g. bilevel gas market models) or models with static or transient gas flow. These embedding structures lead to new challenges in the theoretical analysis (e.g. differentiability, convexity, existence of solutions) as well as in the algorithmic solution (e.g. probabilistic constraints with respect to infinite random inequality systems). A major aspect of the project’s research is the transition from static to dynamic chance constraints.