12/07/2023: ALOP-Colloquium

Lecture: Time-Domain Decomposition for Mixed-Integer Optimal Control Problems (Prof. Dr. Falk Hante, HU Berlin)

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.