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

Sven Leyffer; Paul Manns

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arXiv · 2106.13453

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

Sven Leyffer·Paul Manns

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Abstract

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. We demonstrate the theoretical findings on a computational example.

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Sven Leyffer, Paul Manns. 2021-06-25. Sequential Linear Integer Programming for Integer Optimal Control with Total Variation Regularization. https://arxiv.org/abs/2106.13453

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