Privacy Preservation for Distributed Nonsmooth Constrained Optimization Based on Pseudo-Subgradient

In this paper, we investigate a privacy preservation design in the distributed nonsmooth convex optimization with set constraints. To solve the distributed optimization problem while preserving the privacy, we use pseudo-subgradients involved with (non-integrable) set-valued functions. Based on pseudo-subgradients, we propose distributed nonsmooth optimization algorithms with keeping subgradient information confidential. Then we prove the correctness and convergence of the distributed privacy preservation optimization algorithms to achieve the exact solution of the original optimization problem.