Distributed Nonsmooth Optimization With Coupled Inequality Constraints via Modified Lagrangian Function
Distributed Nonsmooth Optimization With Coupled Inequality Constraints via Modified Lagrangian Function
复制标题
基于修正拉格朗日函数的耦合不等式约束的分布式非光滑优化
DOI：
10.1109/tac.2017.2752001
复制
发表时间：
2018
影响因子：
6.8
通讯作者：
Hong Yiguang
中科院分区：
文献类型：
--
作者：
Liang Shu;Zeng Xianlian;Hong Yiguang
本文考虑具有非光滑成本函数和耦合非线性不等式约束的分布式凸优化问题。为了解决这个问题，我们首先提出了一个包含局部乘子和非平滑罚函数的修正拉格朗日函数。然后，我们利用投影的原始对偶次梯度动力学构建了分布式连续时间算法。基于非光滑分析和Lyapunov函数，我们得到了非光滑算法解的存在性及其收敛性。
This note considers a distributed convex optimization problem with nonsmooth cost functions and coupled nonlinear inequality constraints. To solve the problem, we first propose a modified Lagrangian function containing local multipliers and a nonsmooth penalty function. Then, we construct a distributed continuous-time algorithm by virtue of a projected primal-dual subgradient dynamics. Based on the nonsmooth analysis and Lyapunov function, we obtain the existence of the solution to the nonsmooth algorithm and its convergence.