Distributed Nonsmooth Optimization With Coupled Inequality Constraints via Modified Lagrangian Function

Distributed Nonsmooth Optimization With Coupled Inequality Constraints via Modified Lagrangian Function. Liang, S., Zeng, X., & Hong, Y. IEEE Transactions on Automatic Control, 63(6):1753–1759, June, 2018.

Paper doi abstract bibtex

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.

@article{liang_distributed_2018,
	title = {Distributed {Nonsmooth} {Optimization} {With} {Coupled} {Inequality} {Constraints} via {Modified} {Lagrangian} {Function}},
	volume = {63},
	copyright = {https://ieeexplore.ieee.org/Xplorehelp/downloads/license-information/IEEE.html},
	issn = {0018-9286, 1558-2523},
	url = {https://ieeexplore.ieee.org/document/8036275/},
	doi = {10.1109/TAC.2017.2752001},
	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.},
	language = {en},
	number = {6},
	urldate = {2024-06-18},
	journal = {IEEE Transactions on Automatic Control},
	author = {Liang, Shu and Zeng, Xianlin and Hong, Yiguang},
	month = jun,
	year = {2018},
	keywords = {/unread},
	pages = {1753--1759},
}

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