Distributed Nonsmooth Optimization With Coupled Inequality Constraints via Modified Lagrangian Function

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 distribu...

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Bibliographic Details
Published in:IEEE transactions on automatic control Vol. 63; no. 6; pp. 1753 - 1759
Main Authors: Liang, Shu, Zeng, Xianlin, Hong, Yiguang
Format: Journal Article
Language:English
Published: IEEE 01.06.2018
Subjects:
Algorithm design and analysis
Convergence
Convex functions
Coupled constraint
Distributed algorithms
distributed optimization
Heuristic algorithms
Lagrangian functions
modified Lagrangian function
nonsmooth analysis
Optimization
primal-dual dynamics
ISSN:0018-9286, 1558-2523
Online Access:Get full text
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Summary: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.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2017.2752001