Chance constraints with feedback and integrality (B04)

该项目的目标是将概率约束或机会约束纳入燃气管网优化模型中。这使得人们可以在存在不确定参数(如燃气负荷)的情况下做出规避风险的最优决策。主要应用于具有分层结构的模型(例如，双层天然气市场模型)或具有静态或瞬变气体流动的模型。这些嵌入结构给理论分析(例如解的可微性、凸性、存在性)和算法解(例如关于无限随机不等式系统的概率约束)带来了新的挑战。该项目研究的一个主要方面是从静态机会约束向动态机会约束的过渡。

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.