Exponentially Convergent Algorithm Design for Constrained Distributed Optimization via Nonsmooth Approach

We develop an exponentially convergent distributed algorithm to minimize a sum of nonsmooth cost functions with set constraint. The constraint generally leads the nonlinearity in algorithms, and results difficulties derive exponential rate. In this article, we remove consensus constraints by exact penalty method, then propose projected subgradient virtue differential inclusion differentiated projection operator. Resorting approaches, prove convergence for algorithm, moreover, provide both sublinear rates under some mild assumptions.