论文标题
通过异质延迟进行分布式约束优化的平滑动力学
Smooth Dynamics for Distributed Constrained Optimization with Heterogeneous Delays
论文作者
论文摘要
这项工作从被动性的角度研究了分布式约束的优化问题。首先，我们提出了一种连续的时间算法，用于通过一般凸目标函数进行分布式约束优化。一般凸度下的渐近稳定性由相位铅补偿保证。不平等约束是通过采用无投射的广义拉格朗日人来处理的，其原始双重梯度动力学可保留被动性和平滑性，从而在存在延迟的情况下实现了Lasalle的不变性原理的应用。然后，我们将散射转化纳入提出的算法，以增强针对未知和异质通信延迟的鲁棒性。最后，提供了匹配问题的数值示例来说明结果。
This work investigates the distributed constrained optimization problem under inter-agent communication delays from the perspective of passivity. First, we propose a continuous-time algorithm for distributed constrained optimization with general convex objective functions. The asymptotic stability under general convexity is guaranteed by the phase lead compensation. The inequality constraints are handled by adopting a projection-free generalized Lagrangian, whose primal-dual gradient dynamics preserves passivity and smoothness, enabling the application of the LaSalle's invariance principle in the presence of delays. Then, we incorporate the scattering transformation into the proposed algorithm to enhance the robustness against unknown and heterogeneous communication delays. Finally, a numerical example of a matching problem is provided to illustrate the results.
