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This technical note considers a distributed convex optimization problem withnonsmooth cost functions and coupled nonlinear inequality constraints. To solvethe problem, we first propose a modified Lagrangian function containing localmultipliers and a nonsmooth penalty function. Then we construct a distributedcontinuous-time algorithm by virtue of a projected primal-dual subgradientdynamics. Based on the nonsmooth analysis and Lyapunov function, we obtain theexistence of the solution to the nonsmooth algorithm and its convergence.

Distributed Nonsmooth Optimization with Coupled Inequality Constraints via Modified Lagrangian Function