TY - INPR A1 - Hante, Falk A1 - Krug, Richard A1 - Schmidt, Martin T1 - Time-Domain Decomposition for Mixed-Integer Optimal Control Problems N2 - We consider mixed-integer optimal control problems, whose optimality conditions involve global combinatorial optimization aspects for the corresponding Hamiltonian pointwise in time. We propose a time-domain decomposition, which makes this problem class accessible for mixed-integer programming using parallel-in-time direct discretizations. The approach is based on a decomposition of the optimality system and the interpretation of the resulting subproblems as suitably chosen mixed-integer optimal control problems on subintervals in time. An iterative procedure then ensures continuity of the states at the boundaries of the subintervals via co-state information encoded in virtual controls. We prove convergence of this iterative scheme for discrete-continuous linear-quadratic problems and present numerical results both for linear-quadratic as well as nonlinear problems. KW - Mixed-integer optimal control problems KW - Time-domain decomposition KW - Mixed-integer nonlinear optimization KW - Convergence Y1 - 2021 ER - TY - INPR A1 - Hante, Falk M. A1 - Schmidt, Martin T1 - Gas Transport Network Optimization: Mixed-Integer Nonlinear Models N2 - Although modern societies strive towards energy systems that are entirely based on renewable energy carriers, natural gas is still one of the most important energy sources. This became even more obvious in Europe with Russia's 2022 war against the Ukraine and the resulting stop of gas supplies from Russia. Besides that it is very important to use this scarce resource efficiently. To this end, it is also of significant relevance that its transport is organized in the most efficient, i.e., cost- or energy-efficient, way. The corresponding mathematical optimization models have gained a lot of attention in the last decades in different optimization communities. These models are highly nonlinear mixed-integer problems that are constrained by algebraic constraints and partial differential equations (PDEs), which usually leads to models that are not tractable. Hence, simplifications have to be made and in this chapter, we present a commonly accepted finite-dimensional stationary model, i.e., a model in which the steady-state solutions of the PDEs are approximated with algebraic constraints. For more details about the involved PDEs and the treatment of transient descriptions we refer to Hante and Schmidt (2023). The presented finite-dimensional as well as mixed-integer nonlinear and nonconvex model is still highly challenging if it needs to be solved for real-world gas transport networks. Hence, we also review some classic solution approaches from the literature. KW - Gas networks KW - Mixed-integer nonlinear optimization KW - Mixed-integer linear optimization KW - Nonlinear optimization Y1 - 2023 ER -