Distributed Nonsmooth Optimization with Coupled Inequality Constraints via Modified Lagrangian Function

2016/11/17 by Liang, Shu, Zeng, Xianlin, Hong, Yiguang
#FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1611.05542

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.

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