SIAM Journal on Control and Optimization, Volume 59, Issue 4, Page 2645-2668, January 2021.
Multibang regularization and combinatorial integral approximation decompositions are two actively researched techniques for integer optimal control. We consider a class of polyhedral functions that arise particularly as convex lower envelopes of multibang regularizers and show that they have beneficial properties with respect to regularization of relaxations of integer optimal control problems. We extend the algorithmic framework of the combinatorial integral approximation such that a subsequence of the computed discrete-valued controls converges to the infimum of the regularized integer control problem.

中文翻译：

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组合积分近似的松弛多方正则化

SIAM Journal on Control and Optimization，第 59 卷，第 4 期，第 2645-2668 页，2021 年 1 月。Multibang
正则化和组合积分近似分解是整数优化控制的两种积极研究的技术。我们考虑一类多面体函数，特别是作为 multibang 正则化器的凸下包络出现，并表明它们在整数最优控制问题的松弛正则化方面具有有益的特性。我们扩展了组合积分近似的算法框架，使得计算出的离散值控制的子序列收敛到正则化整数控制问题的下界。