Projection-Free Distributed Optimization With Nonconvex Local Objective Functions and Resource Allocation Constraint

Abstract

We present a novel generalized constrained convex optimization model for multiagent systems that contains both the local, coupled equality, and inequality constraints, and a global resource allocation constraint. This model unifies the traditional constrained optimization problem, the resource allocation problem, and the economic dispatch problem. Unlike the majority of literature where each local objective function is required to be convex, we only require a milder condition that the global objective function is convex. The gradient of the global Lagrangian is estimated locally by each agent using the dynamic average consensus protocol. Synchronously, modified primal-dual dynamics produce the optimal solution via the estimated gradient. The generalized Lagrange multiplier method is introduced to avoid the usual positive projections in the presence of inequality constraints. This leads to smooth dynamics and a continuous Lyapunov derivative, which enables the exponential stability analysis. Simulation examples support the proposed distributed methods.