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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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
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Abstract 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.
AbstractList 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.
Author Xianlin Zeng
Shu Liang
Yiguang Hong
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  surname: Hong
  fullname: Hong, Yiguang
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Snippet This note considers a distributed convex optimization problem with nonsmooth cost functions and coupled nonlinear inequality constraints. To solve the problem,...
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StartPage 1753
SubjectTerms 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
Title Distributed Nonsmooth Optimization With Coupled Inequality Constraints via Modified Lagrangian Function
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