Sequential Linear Integer Programming for Integer Optimal Control with Total Variation Regularization

Understand

We propose a trust-region method that solves a sequence of linear integer programs to tackle integer optimal control problems regularized with a total variation penalty.

• The total variation penalty allows us to prove the existence of minimizers of the integer optimal control problem.
• We introduce a local optimality concept for the problem, which arises from the infinite-dimensional perspective.
• In the case of a one-dimensional domain of the control function, we prove convergence of the iterates produced by our algorithm to points that satisfy first-order stationarity conditions for local optimality.