Primal-dual algorithm for distributed optimization with local domains on signed networks

We consider the distributed optimization problem on signed networks. Each agent has a local function which depends on a subset of the components of the variable and is subject to a local constraint set. A primal-dual algorithm with fixed step size is proposed. The algorithm ensures that the agents' estimates converge to a subset of the components of an optimal solution or its opposite. Note that each component of the variable is allowed to be associated with more than one agents, our algorithm guarantees that those coupled agents achieve bipartite consensus on estimates for the intersection components. Numerical results are provided to demonstrate the theoretical analysis.