Relaxed Multibang Regularization for the Combinatorial Integral Approximation

Manns, Paul

doi:10.1137/20m1377187

Relaxed Multibang Regularization for the Combinatorial Integral Approximation

Journal Article · Thu Jul 15 00:00:00 EDT 2021 · SIAM Journal on Control and Optimization

DOI:https://doi.org/10.1137/20m1377187· OSTI ID:1813096

Manns, Paul ^[1]

Argonne National Lab. (ANL), Lemont, IL (United States)

Multibang regularization and combinatorial integral approximation decompositions are two actively researched techniques for integer optimal control. In this work, 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.

View Accepted Manuscript (DOE)

Research Organization:: Argonne National Laboratory (ANL), Argonne, IL (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: AC02-06CH11357

OSTI ID:: 1813096

Journal Information:: SIAM Journal on Control and Optimization, Journal Name: SIAM Journal on Control and Optimization Journal Issue: 4 Vol. 59; ISSN 0363-0129

Publisher:: Society for Industrial and Applied Mathematics (SIAM)Copyright Statement

Country of Publication:: United States

Language:: English

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