relaxation step

A family of accelerated inexact augmented Lagrangian methods with applications to image restoration

  • Jianchao Bai
  • Yuxue Ma
    • Categories Convex Optimization Tags , , , , ,

    In this paper, we focus on a class of convex optimization problems subject to equality or inequality constraints and have developed an Accelerated Inexact Augmented Lagrangian Method (AI-ALM). Different relative error criteria are designed to solve the subproblem of AI-ALM inexactly, and the popular used relaxation step is exploited to accelerate the convergence. By a … Read more

    A New Insight on Augmented Lagrangian Method with Applications in Machine Learning

  • Jianchao Bai
    • Categories Convex Optimization Tags , , , ,

    Motivated by the work [He-Yuan, Balanced augmented Lagrangian method for convex programming, arXiv: 2108.08554v1, (2021)], a novel augmented Lagrangian method with a relaxation step is proposed for solving a family of convex optimization problem subject to equality or inequality constraint. This new method is then extended to solve the multi-block separable convex optimization problem, and … Read more