Time-Domain Decomposition for Mixed-Integer Optimal Control Problems

Hante FM, Krug R, Schmidt M (2023)

Publication Type: Journal article

Publication year: 2023

Journal

Applied Mathematics and Optimization Springer Verlag (Germany)

Book Volume: 87

Article Number: 36

Journal Issue: 3

DOI: 10.1007/s00245-022-09949-x

Abstract

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.

Authors with CRIS profile

Richard Krug Sonderforschungsbereich/Transregio 154: Mathematische Modellierung, Simulation und Optimierung am Beispiel von Gasnetzwerken

Involved external institutions

Universität Trier DE Germany (DE) Humboldt-Universität zu Berlin DE Germany (DE)

How to cite

APA:

Hante, F.M., Krug, R., & Schmidt, M. (2023). Time-Domain Decomposition for Mixed-Integer Optimal Control Problems. Applied Mathematics and Optimization, 87(3). https://doi.org/10.1007/s00245-022-09949-x

MLA:

Hante, Falk M., Richard Krug, and Martin Schmidt. "Time-Domain Decomposition for Mixed-Integer Optimal Control Problems." Applied Mathematics and Optimization 87.3 (2023).

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