Hybrid protocol for distributed non-differentiable extended monotropic optimization

This paper presents a hybrid protocol design for distributed non-differentiable extended monotropic optimization problems, which have various applications in large-scale optimization and evolutionary computation. The considered objective function is the sum of local non-differentiable objective functions, which are assigned to different agents in multi-agent networks, with local set constraints and affine equality constraints. Each agent can only access to its local non-differentiable objective function, local set constraint and equality constraint, and exchange information with its neighbors to obtain the global optimal solution. For this type of optimization problems, we propose a distributed state-dependent hybrid method over multi-agent networks. In addition, we properly design the jump map and jump set to improve the transient performance and accelerate the consensus process of existing distributed continuous-time methods. With invariance principle of hybrid dynamical systems, we prove that the proposed hybrid protocol converges to the global optimal solution. We verify that the proposed hybrid method has a good convergence property and transient performance through numerical experiments.