A distributed semismooth Newton based augmented Lagrangian method for distributed optimization

2026-02-27

AI Summary

This work addresses a distributed optimization problem where agents in a network communicate only with their neighbors and aim to minimize the sum of local cost functions. The problem is equivalently reformulated in a constrained form, and a solution framework based on the augmented Lagrangian is developed. The key innovation lies in integrating a semismooth Newton method with a distributed accelerated proximal gradient algorithm, leveraging the structure of the generalized Hessian to avoid transmitting full Hessian matrices, thereby achieving efficient communication and computation. Theoretical analysis establishes the convergence of the proposed algorithm, and numerical experiments demonstrate its superior performance in terms of convergence speed and overall efficiency compared to existing distributed methods.

Technology Category

• Search and Optimization: Distributed Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Multiagent Systems: Distributed Problem Solving

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

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.

Problem

• distributed optimization
• networked systems
• constrained optimization
• local cost functions
• neighbor communication

Innovation

• distributed optimization
• semismooth Newton method
• augmented Lagrangian
• generalized Hessian
• accelerated proximal gradient