Distributed Nonsmooth Optimization with Coupled Inequality Constraints via Modified Lagrangian Function

Shu Liang; Xianlin Zeng; Yiguang Hong

Distributed Nonsmooth Optimization with Coupled Inequality Constraints via Modified Lagrangian Function

Optimization and Control 2017-05-09 v2

Authors: Shu Liang , Xianlin Zeng , Yiguang Hong

Abstract

This technical 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.

Keywords

distributed optimization proximal optimization primal-dual optimization

Cite

@article{arxiv.1611.05542,
  title  = {Distributed Nonsmooth Optimization with Coupled Inequality Constraints via Modified Lagrangian Function},
  author = {Shu Liang and Xianlin Zeng and Yiguang Hong},
  journal= {arXiv preprint arXiv:1611.05542},
  year   = {2017}
}

Comments

4 figures, 2 table

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