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arXiv · 2610.02433

Accelerated Safe Gradient Flow

Xuting Gao·Sonia Martínez
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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.

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Xuting Gao, Sonia Martínez. 2026-10-01. Accelerated Safe Gradient Flow. https://arxiv.org/abs/2610.02433

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