Prescribed-time distributed optimization problem with constraints

In recent years, distributed optimization problem have a wide range of applications in various fields. This paper considers the prescribed-time distributed optimization problem with/without constraints. Firstly, we assume the state of each agent is constrained, and the prescribed-time distributed optimization algorithm with constraints is designed on the basis of gradient projection algorithm and consensus algorithm. Secondly, the constrained distributed optimization problem is transformed into the unconstrained distributed optimization problem, and according to the gradient descent algorithm and consensus algorithm, we also propose the prescribed-time distributed optimization algorithm without constraints. By designing the appropriate objective functions, we prove the multi-agent system can converge to the optimal solution within any prescribed-time, and the convergence time is fully independent of the initial conditions and system parameters. Finally, three simulation examples are provided to verify the validity of the designed algorithms.