A distributed semismooth Newton based augmented Lagrangian method for distributed optimization

• URL: http://arxiv.org/abs/2602.23854v1
• Date: Fri, 27 Feb 2026 09:52:59 GMT
• Title: A distributed semismooth Newton based augmented Lagrangian method for distributed optimization
• Authors: Qihao Ma, Chengjing Wang, Peipei Tang, Dunbiao Niu, Aimin Xu,
• Abstract summary: We employ the augmented Lagrangian method to solve an equivalently reformulated constrained version of the original problem.<n>Each resulting subproblem is solved inexactly via a distributed semismooth Newton method.<n>By fully leveraging the structure of the generalized Hessian, a distributed accelerated proximal gradient method is proposed to compute the Newton direction efficiently.
• Score: 0.21748200848556345
• License: http://creativecommons.org/publicdomain/zero/1.0/
• 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.

Related papers

• Alternating Iteratively Reweighted $\ell_1$ and Subspace Newton Algorithms for Nonconvex Sparse Optimization [11.56128809794923]
  We present a novel hybrid algorithm for minimizing the sum of a differentiable loss function and a nonsmooth regularization function.<n>We prove global convergence to a critical point and, under suitable conditions, demonstrate that the algorithm outperforms existing methods.
  arXiv  Detail & Related papers  (2024-07-24T12:15:59Z)
• Distributed Markov Chain Monte Carlo Sampling based on the Alternating Direction Method of Multipliers [143.6249073384419]
  In this paper, we propose a distributed sampling scheme based on the alternating direction method of multipliers. We provide both theoretical guarantees of our algorithm's convergence and experimental evidence of its superiority to the state-of-the-art. In simulation, we deploy our algorithm on linear and logistic regression tasks and illustrate its fast convergence compared to existing gradient-based methods.
  arXiv  Detail & Related papers  (2024-01-29T02:08:40Z)
• Network-GIANT: Fully distributed Newton-type optimization via harmonic Hessian consensus [2.8617826964327113]
  We introduce a Newton-type fully distributed optimization algorithm, Network-GIANT, based on GIANT. We prove that our algorithm guarantees semi-global and exponential convergence to the exact solution over the network assuming strongly convex and smooth loss functions. We provide empirical evidence of the superior convergence performance of Network-GIANT over other state-of-art distributed learning algorithms such as Network-DANE and Newton-Raphson Consensus.
  arXiv  Detail & Related papers  (2023-05-13T11:42:40Z)
• Linearization Algorithms for Fully Composite Optimization [61.20539085730636]
  This paper studies first-order algorithms for solving fully composite optimization problems convex compact sets. We leverage the structure of the objective by handling differentiable and non-differentiable separately, linearizing only the smooth parts.
  arXiv  Detail & Related papers  (2023-02-24T18:41:48Z)
• Robust empirical risk minimization via Newton's method [9.797319790710711]
  A new variant of Newton's method for empirical risk minimization is studied. The gradient and Hessian of the objective function are replaced by robust estimators. An algorithm for obtaining robust Newton directions based on the conjugate gradient method is also proposed.
  arXiv  Detail & Related papers  (2023-01-30T18:54:54Z)
• Fast Computation of Optimal Transport via Entropy-Regularized Extragradient Methods [75.34939761152587]
  Efficient computation of the optimal transport distance between two distributions serves as an algorithm that empowers various applications. This paper develops a scalable first-order optimization-based method that computes optimal transport to within $varepsilon$ additive accuracy.
  arXiv  Detail & Related papers  (2023-01-30T15:46:39Z)
• Quantization-Based Optimization: Alternative Stochastic Approximation of Global Optimization [0.0]
  We propose a global optimization algorithm based on quantizing the energy level of an objective function in an NP-hard problem. Numerical experiments show that the proposed algorithm outperforms conventional learning methods in solving NP-hard optimization problems.
  arXiv  Detail & Related papers  (2022-11-08T03:01:45Z)
• First-Order Algorithms for Nonlinear Generalized Nash Equilibrium Problems [88.58409977434269]
  We consider the problem of computing an equilibrium in a class of nonlinear generalized Nash equilibrium problems (NGNEPs) Our contribution is to provide two simple first-order algorithmic frameworks based on the quadratic penalty method and the augmented Lagrangian method. We provide nonasymptotic theoretical guarantees for these algorithms.
  arXiv  Detail & Related papers  (2022-04-07T00:11:05Z)
• A Stochastic Newton Algorithm for Distributed Convex Optimization [62.20732134991661]
  We analyze a Newton algorithm for homogeneous distributed convex optimization, where each machine can calculate gradients of the same population objective. We show that our method can reduce the number, and frequency, of required communication rounds compared to existing methods without hurting performance.
  arXiv  Detail & Related papers  (2021-10-07T17:51:10Z)
• IDEAL: Inexact DEcentralized Accelerated Augmented Lagrangian Method [64.15649345392822]
  We introduce a framework for designing primal methods under the decentralized optimization setting where local functions are smooth and strongly convex. Our approach consists of approximately solving a sequence of sub-problems induced by the accelerated augmented Lagrangian method. When coupled with accelerated gradient descent, our framework yields a novel primal algorithm whose convergence rate is optimal and matched by recently derived lower bounds.
  arXiv  Detail & Related papers  (2020-06-11T18:49:06Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.