Distributed continuous‐time constrained convex optimization with general time‐varying cost functions
Bomin Huang, Yao Zou, Ziyang Meng · International Journal of Robust and Nonlinear Control · 2020
Abstract The distributed time‐varying constrained convex optimization problem over a connected undirected network topology is studied in this article. The proposed distributed optimization algorithm is composed of a projection map term, a consensus term, and a gradient term, and is feasible for any initial condition. We first show that the states of the optimization algorithm uniformly converge to a neighborhood of the constraint set while an approximate global consensus is achieved. Then the states are proven to uniformly converge to a neighborhood of the time‐varying optimal trajectory. The theoretical results are validated by some simulations.