On the Regularization of Primal-Dual Dynamics in Time-Dependent Nonconvex Optimization
Miguel Vaquero, J. Cortés
arXiv preprint arXiv:2610.19916 · 2026
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.