Distributed Continuous-time Nonsmooth Optimization with Coupled Nonlinear Inequality Constraints

In this paper, we consider a distributed convex optimization problem with nonsmooth cost functions and coupled nonlinear inequality constraints. To solve the problem, we first propose a novel Lagrangian function and then construct a distributed continuous-time algorithm by virtue of a gradient-decent-gradient-ascent saddle-point dynamics. We carry out the distributed design by using local multipliers to overcome difficulties resulting from the coupled constraints and employing a nonsmooth penalty function to ensure the correctness. Based on nonsmooth analysis and Lyapunov function, we obtain the existence of solution to the nonsmooth algorithm and its convergence.

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