Chance constraints with feedback and integrality (B04)

该项目的目标是将概率或机会约束纳入天然气网络优化模型。这允许人们在不确定参数（如气体负荷）存在的情况下采取规避风险的最佳决策。主要应用于具有层次结构的模型（例如双层气体市场模型）或具有静态或瞬态气体流动的模型。这些嵌入结构给理论分析（如可微性、凸性、解的存在性）和算法解决（如关于无限随机不等式系统的概率约束）带来了新的挑战。项目研究的一个主要方面是从静态机会约束到动态机会约束的转变。

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.