论文标题
有限时间收敛算法，用于时变的分布式优化
Finite-Time Convergent Algorithms for Time-Varying Distributed Optimization
论文作者
论文摘要
本文着重于有限时间（FT）收敛分布式算法，用于解决时变（TV）分布式优化（TVDO）。目的是最大程度地减少通过在有限时间内的多个代理商协调可能会受到电视限制的本地电视成本功能的总和。具体而言，研究了两类TVDO，其中包括无约束的分布式共识优化和分布式最佳资源分配问题（DORAP），以及电视成本功能和耦合方程约束。对于前一个，基于非平滑分析，基于使用局部辅助子系统的扩展零梯度和方法提出了连续的时间分布式不连续的动力学。然后，通过双重变换进一步获得了ft收敛的分布式动力学。特别是，在双重变量的动力学中，不需要对成本函数的Hessians的反转，而需要求解另一种局部优化以在每次瞬间获得原始变量。最后，进行了两个数值示例以验证所提出的算法。
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.
