Sequential Integer Linear Programming with Accelerations by Shortest Path Computations for Integer Optimal Control on One-dimensional Domains

JP Dr. Paul Manns

Chair of Numerical Analysis and Optimization, Faculty of Mathematics, TU Dortmund University

Tuesday, March 01, 2022, 11:00 - 12:00


We consider optimal control problems on one-dimensional domains that are regularized by a switching cost penalty in the objective. Since these problems cannot be treated with computationally very efficient relaxation-based algorithms like the combinatorial integral approximation with sum-up rounding, we propose a trust-region algorithm, in which the subproblems are again integer control problems. Under suitable assumptions the trust-region algorithm produces iterates that converge to a first-order optimal control, for which we obtain a characterization by means of its switching points. After discretization the subproblems become integer linear programs. We show that the latter can be solved efficiently with an accelerated Dijkstra's algorithm that incorporates dual information on the subproblem.

Collaborators: Sven Leyffer (Argonne National Laboratory), Marvin Severitt (TU Dortmund)

Slides can be found here: slides.pdf
Meeting-ID: 627 9173 7415
Password: syscop2021