As part of the colloquium of the Research Training Group Algorithmic Optimization will take place on

Thursday, December 07, 2023 16:00 c.t. Lecture hall 9

the following lecture will take place:

Time-Domain Decomposition for Mixed-Integer Optimal Control Problems

Prof. Dr. Falk Hante, HU Berlin

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.