Distributed Nonsmooth Optimization With Coupled Inequality Constraints via Modified Lagrangian Function

被引：132

作者：

Liang, Shu ^{[1
]}

Zeng, Xianlin ^{[2
]}

Hong, Yiguang ^{[3
,4
]}

机构：

[1] Univ Sci & Technol Beijing, Sch Automat & Elect Engn, Beijing 100083, Peoples R China

[2] Beijing Inst Technol, Sch Automat, Beijing 100081, Peoples R China

[3] Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Syst & Control, Beijing 100190, Peoples R China

[4] Univ Chinese Acad Sci, Beijing 100190, Peoples R China

来源：

IEEE TRANSACTIONS ON AUTOMATIC CONTROL | 2018年 / 63卷 / 06期

基金：

中国国家自然科学基金;

关键词：

Coupled constraint; distributed optimization; modified Lagrangian function; nonsmooth analysis; primal-dual dynamics; ECONOMIC-DISPATCH; SYSTEMS; COORDINATION; CONVERGENCE; DYNAMICS; NETWORK;

D O I：

10.1109/TAC.2017.2752001

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

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 sub-gradient dynamics. Based on the nonsmooth analysis and Lyapunov function, we obtain the existence of the solution to the nonsmooth algorithm and its convergence.

引用

页码：1753 / 1759

页数：7

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