Finite-Time Convergent Algorithms for Time-Varying Distributed Optimization

TL;DR

This paper develops finite-time convergent distributed algorithms for solving time-varying optimization problems, including consensus and resource allocation, with theoretical guarantees and numerical validation.

Contribution

It introduces novel continuous-time distributed algorithms achieving finite-time convergence for time-varying optimization, including dual transformation techniques that avoid Hessian inversion.

Findings

Algorithms achieve finite-time convergence in simulations.

Proposed methods handle time-varying cost functions and constraints.

Numerical examples verify effectiveness and convergence.

Abstract

This paper focuses on finite-time (FT) convergent distributed algorithms for solving time-varying (TV) distributed optimization (TVDO). The objective is to minimize the sum of local TV cost functions subject to the possible TV constraints by the coordination of multiple agents in finite time. Specifically, two classes of TVDO are investigated included unconstrained distributed consensus optimization and distributed optimal resource allocation problems (DORAP) with both TV cost functions and coupled equation constraints. For the previous one, based on non-smooth analysis, a continuous-time distributed discontinuous dynamics with FT convergence is proposed based on an extended zero-gradient-sum method with a local auxiliary subsystem. Then, an FT convergent distributed dynamics is further obtained for TV-DORAP by dual transformation. Particularly, the inversion of the cost functions' Hessians is not required in the dual variables' dynamics, while another local optimization needs to be solved to obtain the primal variable at each time instant. Finally, two numerical examples are conducted to verify the proposed algorithms.