DAOCP: a dual active set solver for optimal control problems
Abstract
We present DAOCP, a dual active set solver for linear quadratic optimal control problems with stage-wise equality and inequality constraints. Active set methods are leading Model Predictive Control benchmarks for full-body robotics, but existing solvers operate on dense QPs, while typical problem dimensions favor methods that exploit the optimal control structure. DAOCP combines the warm-starting capabilities of active set algorithms with the better computational scaling of structure exploiting solvers, by relying on a generalization of the relationship between the Riccati recursion and the Cholesky factorization of the condensed Hessian. This result enables dual active set iterations to operate directly on the original optimal control problem through recursive computations, without explicitly forming the condensed quadratic program. On robotics benchmarks, DAOCP is the fastest of four solvers in four of five scenarios, cutting average solve time on a 58-state Atlas model by 9× relative to state of the art solvers DAQP and HPIPM.
Related
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BibTeX
@misc{zaupa2026daocp,
title = {{DAOCP: a dual active set solver for optimal control problems}},
author = {Alberto Zaupa and Samuel Erickson and Mikael Johansson},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.33451},
eprint = {2609.33451},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.33451},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - DAOCP: a dual active set solver for optimal control problems
AU - Alberto Zaupa
AU - Samuel Erickson
AU - Mikael Johansson
PY - 2026
DA - 2026/09/27
PB - arXiv
DO - 10.48550/arxiv.2609.33451
UR - https://arxiv.org/abs/2609.33451
AB - We present DAOCP, a dual active set solver for linear quadratic optimal control problems with stage-wise equality and inequality constraints. Active set methods are leading Model Predictive Control benchmarks for full-body robotics, but existing solvers operate on dense QPs, while typical problem dimensions favor methods that exploit the optimal control structure. DAOCP combines the warm-starting capabilities of active set algorithms with the better computational scaling of structure exploiting solvers, by relying on a generalization of the relationship between the Riccati recursion and the Cholesky factorization of the condensed Hessian. This result enables dual active set iterations to operate directly on the original optimal control problem through recursive computations, without explicitly forming the condensed quadratic program. On robotics benchmarks, DAOCP is the fastest of four solvers in four of five scenarios, cutting average solve time on a 58-state Atlas model by 9× relative to state of the art solvers DAQP and HPIPM.
ER -