Distributed Finite-Time Optimization Algorithm for Time-Varying Cost Functions Based on Multi-agent Systems

This paper introduces a distributed finite-time optimization approach for convex optimization with time-varying cost function in multi-agent systems under an undirected and connected communication graph. Unlike most existing optimization problems with constant optimal solutions and local time-invariant cost functions, a distributed optimization problem herein has time-varying optimal solutions and time-varying cost functions. Utilizing predefined-time consensus and a Hessian-based predictive correction method, the proposed distributed optimization algorithm guarantees simultaneous achievement of agent state synchronization within a user-specified time window and finite-time minimization of the temporally varying global performance metric. Finally, a numerical example is presented to validate the effectiveness of the proposed algorithm.