On the Regularization of Primal-Dual Dynamics in Time-Dependent Nonconvex Optimization
Abstract
We study continuous-time primal-dual dynamics for tracking solutions of time-dependent constrained optimization problems. First, for uniformly strongly convex-strongly concave saddle functions, we establish explicit finite-time tracking and additive-disturbance bounds. For convex problems, we then introduce a directional primal regularization, combined with dual Tikhonov regularization, and quantify the resulting optimization bias and constraint violation. For smooth nonconvex problems, we couple a proximal local convexification with a two-time-scale primal-dual flow and obtain a local tracking result under constraint qualification, second-order sufficiency, and temporal regularity. Numerical traffic-signal experiments at a single intersection evaluate the proposed method under vehicle-throughput and pedestrian-aware objectives, comparing it with standard signal-control schemes.
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BibTeX
@misc{vaquero2026regularization,
title = {{On the Regularization of Primal-Dual Dynamics in Time-Dependent Nonconvex Optimization}},
author = {Miguel Vaquero and Jorge Cortés},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.19916},
eprint = {2610.19916},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.19916},
}
RIS
TY - UNPB
TI - On the Regularization of Primal-Dual Dynamics in Time-Dependent Nonconvex Optimization
AU - Miguel Vaquero
AU - Jorge Cortés
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.19916
UR - https://arxiv.org/abs/2610.19916
AB - We study continuous-time primal-dual dynamics for tracking solutions of time-dependent constrained optimization problems. First, for uniformly strongly convex-strongly concave saddle functions, we establish explicit finite-time tracking and additive-disturbance bounds. For convex problems, we then introduce a directional primal regularization, combined with dual Tikhonov regularization, and quantify the resulting optimization bias and constraint violation. For smooth nonconvex problems, we couple a proximal local convexification with a two-time-scale primal-dual flow and obtain a local tracking result under constraint qualification, second-order sufficiency, and temporal regularity. Numerical traffic-signal experiments at a single intersection evaluate the proposed method under vehicle-throughput and pedestrian-aware objectives, comparing it with standard signal-control schemes.
ER -