A subgradient-based continuous-time algorithm for constrained distributed quadratic programming

In this paper, a constrained distributed quadratic programming over a directed graph is studied. Inspired by iterative idea, a smooth penalty-based quadratic programming problem is proposed. To solve the penalty-based quadratic programming problem, a novel distributed subgradient-based continuous-time algorithm is presented. With the help of Łojasiewicz inequality, the state solution of the presented algorithm is proved to be exponentially convergent to a Karush–Kuhn–Tucker (KKT) point of the smooth penalty-based quadratic programming. It should be noted that the exponential convergence of the presented algorithm is independent of strong convexity of objective functions. In particular, the finite-time convergence is obtained when the considered optimization problem is degenerated to a linear one. Finally, one numerical example and the application to robust estimation in wireless sensor networks are shown to verify the effectiveness of the proposed algorithm.