Accelerated Safe Gradient Flow
Abstract
This letter introduces an accelerated safe gradient flow (A-SGF) for strongly convex constrained optimization problems. The A-SGF filters a nominal second-order accelerated flow through a second-order control barrier function quadratic program. We establish conditions for strict feasibility and local Lipschitz continuity of the resulting vector field, prove forward invariance of a lifted safe set, and show that its unique equilibrium is the constrained minimizer. A variational Lyapunov analysis isolates the effect of the safety correction and gives explicit conditions on the barrier gains under which A-SGF retains the same convergence rate as the unconstrained Nesterov accelerated method. A nonlinear 2D example demonstrate anytime feasibility and faster convergence of the algorithm.
Related
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BibTeX
@misc{gao2026accelerated,
title = {{Accelerated Safe Gradient Flow}},
author = {Xuting Gao and Sonia Martínez},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.02433},
eprint = {2610.02433},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.02433},
}
RIS
TY - UNPB
TI - Accelerated Safe Gradient Flow
AU - Xuting Gao
AU - Sonia Martínez
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.02433
UR - https://arxiv.org/abs/2610.02433
AB - This letter introduces an accelerated safe gradient flow (A-SGF) for strongly convex constrained optimization problems. The A-SGF filters a nominal second-order accelerated flow through a second-order control barrier function quadratic program. We establish conditions for strict feasibility and local Lipschitz continuity of the resulting vector field, prove forward invariance of a lifted safe set, and show that its unique equilibrium is the constrained minimizer. A variational Lyapunov analysis isolates the effect of the safety correction and gives explicit conditions on the barrier gains under which A-SGF retains the same convergence rate as the unconstrained Nesterov accelerated method. A nonlinear 2D example demonstrate anytime feasibility and faster convergence of the algorithm.
ER -