Distributed multi-agent optimization with inequality constraints and random projections

In this paper, we consider a multi-agent convex optimization problem whose goal is to minimize a global convex objective function that is the sum of local convex objective functions, subject to global convex inequality constraints and several randomly occurring local convex state constraint sets. A distributed primal-dual random projection subgradient (DPDRPS) algorithm with diminishing stepsize using local communications and computations is proposed to solve such a problem. By employing iterative inequality techniques, the proposed DPDRPS algorithm is proved to be convergent almost surely. Finally, a numerical example is illustrated to show the effectiveness of the theoretical analysis.