A Fixed-time Distributed Constrained Optimization Algorithm over Weight-unbalanced Directed Network

This paper mainly studies the solution of distributed constrained optimization problems over unbalanced directed systems. First, we design a fixed-time consensus strategy via symbolic function to obtain the left eigenvalues of the corresponding Laplacian matrices of the communication network within a fixed time. Then, we develop a novel distributed constraint optimization method without initial constraints based on symbolic functions. The developed method claims that the optimal solution can be achieved within a fixed time based on the continuous-time Lyapunov stability theory. Finally, a set of simulation cases is given to illustrate the practicality of the developed method.