Exponential Convergence of Primal-Dual Dynamical System for Linear Constrained Optimization

Primal-dual dynamics (PDD) and its variants are prominent first-order continuous-time algorithms to determine the primal and dual solutions of a constrained optimization problem (COP). Due to the simple structure, they have received widespread attention in various fields, such as distributed optimization [1], power systems [2], and wireless communication [3]. In view of their wide applications, there are numerous theoretic studies on the convergence properties of PDD and its variants, including the exponential stability analysis [4]–[9].