A distributed semismooth Newton based augmented Lagrangian method for distributed optimization
It addresses optimization problems for networked systems where agents have local cost functions and limited communication, representing an incremental improvement over existing distributed algorithms.
The paper tackles distributed optimization over networks by proposing a novel algorithm that combines semismooth Newton and augmented Lagrangian methods, achieving efficient convergence and outperforming state-of-the-art methods in numerical experiments.
This paper proposes a novel distributed semismooth Newton based augmented Lagrangian method for solving a class of optimization problems over networks, where the global objective is defined as the sum of locally held cost functions, and communication is restricted to neighboring agents. Specifically, we employ the augmented Lagrangian method to solve an equivalently reformulated constrained version of the original problem. Each resulting subproblem is solved inexactly via a distributed semismooth Newton method. By fully leveraging the structure of the generalized Hessian, a distributed accelerated proximal gradient method is proposed to compute the Newton direction efficiently, eliminating the need to communicate with full Hessian matrices. Theoretical results are also obtained to guarantee the convergence of the proposed algorithm. Numerical experiments demonstrate the efficiency and superiority of our algorithm compared to state-of-the-art distributed algorithms.