An approximate gradient algorithm for constrained distributed convex optimization

In this paper, we propose an approximate gradient algorithm for the multi-agent convex optimization problem with constraints. The agents cooperatively compute the minimum of the sum of the local objective functions which are subject to a global inequality constraint and a global constraint set. Instead of each agent can get exact gradient, as discussed in the literature, we only use approximate gradient with some computation or measurement errors. The gradient accuracy conditions are presented to ensure the convergence of the approximate gradient algorithm. Finally, simulation results demonstrate good performance of the approximate algorithm.