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Multibang regularization and combinatorial integral approximationdecompositions are two actively researched techniques for integer optimalcontrol. We consider a class of polyhedral functions that arise particularly asconvex lower envelopes of multibang regularizers and show that they havebeneficial properties with respect to regularization of relaxations of integeroptimal control problems. We extend the algorithmic framework of thecombinatorial integral approximation such that a subsequence of the computeddiscrete-valued controls converges to the infimum of the regularized integercontrol problem.

Relaxed multibang regularization for the combinatorial integral approximation