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Domain Decomposition for Integer Optimal Control with Total Variation Regularization

Journal Article · · SIAM Journal on Control and Optimization
DOI:https://doi.org/10.1137/24M170466X· OSTI ID:3006563
 [1];  [2]
  1. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
  2. Technische Univ. of Dortmund (Germany)
+ Show Author Affiliations
Total variation integer optimal control problems admit solutions and necessary optimality conditions via geometric variational analysis. In spite of the existence of said solutions, algorithms which solve the discretized objective suffer from high numerical cost associated with the combinatorial nature of integer programming. Hence, such methods are often limited to small and medium-sized problems. We propose a globally convergent, coordinate descent–inspired algorithm that allows tractable subproblem solutions restricted to a partition of the domain. Our decomposition method solves relatively small trust-region subproblems that modify the control variable on a subdomain only. Given nontrivial subdomain overlap, we prove that a global first-order necessary optimality condition is equivalent to a first-order necessary optimality condition per subdomain. We additionally show that a sufficient decrease is achieved on a single subdomain by way of a trust-region subproblem solver using geometric measure–theoretic arguments, which we integrate with a greedy patch selection to prove convergence of our algorithm. In conclusion, we demonstrate the practicality of our algorithm on a benchmark large-scale, PDE-constrained integer optimal control problem and find that our method is faster than the state of the art.
Research Organization:
Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
Sponsoring Organization:
USDOE National Nuclear Security Administration (NNSA); Deutsche Forschungsgemeinschaft (DFG); US Air Force Office of Scientific Research (AFOSR)
Grant/Contract Number:
NA0003525
OSTI ID:
3006563
Report Number(s):
SAND--2025-14941J; 1761252
Journal Information:
SIAM Journal on Control and Optimization, Journal Name: SIAM Journal on Control and Optimization Journal Issue: 6 Vol. 63; ISSN 0363-0129; ISSN 1095-7138
Publisher:
Society for Industrial and Applied Mathematics (SIAM)Copyright Statement
Country of Publication:
United States
Language:
English

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Related Subjects

domain decomposition
integer optimal control
total variation regularization
trust-region methods