In this paper we develop a multi-agent distributed algorithm to solve a quadratic programming problem with linear time-varying constraints. In more detail, we first solve the frozen-time optimization problem, providing a necessary and sufficient global optimality condition. Then, based on such condition we develop a continuous-time nonsmooth algorithm that is able to track the time-varying global optimal solution in finite-time. The proposed algorithm requires 2-hop neighborhood information that can be estimated by resorting to a state-of-the art finite-time k-hop distributed observer which can be implemented using only 1-hop information. Numerical results are provided to corroborate the theoretical findings.
Santilli, M., Oliva, G., Gasparri, A. (2020). Distributed Finite-Time Algorithm for a Class of Quadratic Optimization Problems with Time-Varying Linear Constraints. In Proceedings of the IEEE Conference on Decision and Control (pp.4380-4386). Institute of Electrical and Electronics Engineers Inc. [10.1109/CDC42340.2020.9304300].