An Adaptive, Parallel, and Inexact Newton Method for Large-scale Nonlinear Optimal Control
Abstract
We design adaptive overlapping temporal decomposition (AOTD), a parallel sequential quadratic programming (SQP) method for long-horizon nonlinear optimal control problems (OCPs). As designed, AOTD is the first overlapping temporal decomposition (OTD) algorithm that adapts the overlap size online, eliminating the need to fix a suitable overlap a priori. Specifically, at each iteration, it partitions the long horizon into overlapping nonlinear subproblems, performs one SQP step on each in parallel, and adaptively selects both the overlap size and the accuracy to which the resulting local KKT systems are solved. Two conditions govern the accepted step: an adaptive residual condition bounding the distance from the concatenated inexact direction to the exact Newton direction of the full problem, and a descent condition on the adaptive penalty parameters that certifies descent for a carefully chosen exact augmented Lagrangian. The residual condition is solver independent and accommodates both deterministic iterative solvers and randomized sketching solvers. Under standard regularity assumptions, we prove that the KKT residual converges to zero from any initialization and establish a local linear rate for sequences converging to a strict local minimizer. We validate AOTD on a power-system frequency regulation OCP and a Burgers PDE OCP, attaining a reduction in estimated FLOPs of approximately 2.5× to the best fixed-overlap variant while converging across multiple horizon lengths with a single parameter setting.
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BibTeX
@misc{bhan2026adaptive,
title = {{An Adaptive, Parallel, and Inexact Newton Method for Large-scale Nonlinear Optimal Control}},
author = {Luke Bhan and Michael W. Mahoney and Sen Na},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.33206},
eprint = {2609.33206},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.33206},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - An Adaptive, Parallel, and Inexact Newton Method for Large-scale Nonlinear Optimal Control
AU - Luke Bhan
AU - Michael W. Mahoney
AU - Sen Na
PY - 2026
DA - 2026/09/27
PB - arXiv
DO - 10.48550/arxiv.2609.33206
UR - https://arxiv.org/abs/2609.33206
AB - We design adaptive overlapping temporal decomposition (AOTD), a parallel sequential quadratic programming (SQP) method for long-horizon nonlinear optimal control problems (OCPs). As designed, AOTD is the first overlapping temporal decomposition (OTD) algorithm that adapts the overlap size online, eliminating the need to fix a suitable overlap a priori. Specifically, at each iteration, it partitions the long horizon into overlapping nonlinear subproblems, performs one SQP step on each in parallel, and adaptively selects both the overlap size and the accuracy to which the resulting local KKT systems are solved. Two conditions govern the accepted step: an adaptive residual condition bounding the distance from the concatenated inexact direction to the exact Newton direction of the full problem, and a descent condition on the adaptive penalty parameters that certifies descent for a carefully chosen exact augmented Lagrangian. The residual condition is solver independent and accommodates both deterministic iterative solvers and randomized sketching solvers. Under standard regularity assumptions, we prove that the KKT residual converges to zero from any initialization and establish a local linear rate for sequences converging to a strict local minimizer. We validate AOTD on a power-system frequency regulation OCP and a Burgers PDE OCP, attaining a reduction in estimated FLOPs of approximately 2.5× to the best fixed-overlap variant while converging across multiple horizon lengths with a single parameter setting.
ER -