Distributed Algorithm for Time-varying Convex Optimization with Fixed-time Convergence

Distributed time-varying (TV) convex optimization has wide applications in coordinating multiple mobile robots and sensing networks. The global cost function varies over time and is allocated to multiple agents, each communicating with neighbors to solve the global problem. Pioneering works have relied on identical Hessian matrices and time derivatives of the gradient. This paper proposes a solution to the issue by designing a distributed algorithm that integrates distributed average tracking techniques with the prediction-correction interior point method. Specifically, we present a Distributed Prediction-Correction Algorithm with Fractional-Order Dynamics, which attains fixed-time convergence without necessitating real-time computation of partial time derivatives of the gradient. Numerical simulations demonstrate the efficacy of the proposed algorithm.