Jianchao Bai

A new insight on the prediction-correction framework with applications to first-order methods

  • Jianchao Bai
    • Categories Convex and Nonsmooth Optimization, Global Optimization

    The prediction-correction framework developed in [B. He, Splitting Contraction Algorithm for Convex Optimization, Science Press, 2025] is a simple yet powerful tool for analyzing the convergence of diverse first-order optimization methods, including the Augmented Lagrangian Method (ALM) and the Alternating Direction Method of Multipliers (ADMM). In this paper, we propose a generalized prediction-correction framework featuring … Read more

    A strongly convergent projection and contraction algorithm with extrapolations from the past

  • Jianchao Bai
    • Categories Nonsmooth Optimization Tags , , ,

    This paper introduces a projection and contraction-type algorithm that features an extrapolation from the past, reducing the two values of the cost operator inherent in the original projection and contraction algorithm to a single value at the current iteration. Strong convergence results of the proposed algorithm are proved in Hilbert spaces. Experimental results on testing … Read more

    A double-accelerated proximal augmented Lagrangian method with applications in signal reconstruction

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

    The Augmented Lagrangian Method (ALM), firstly proposed in 1969, remains a vital framework in large-scale constrained optimization. This paper addresses a linearly constrained composite convex minimization problem and presents a general proximal ALM that incorporates both Nesterov acceleration and relaxed acceleration, while enjoying indefinite proximal terms. Under mild assumptions (potentially without requiring prior knowledge of … Read more

    A proximal-perturbed Bregman ADMM for solving nonsmooth and nonconvex optimization problems

  • Jianchao Bai
    • Categories Nonsmooth Optimization Tags , , ,

    In this paper, we focus on a linearly constrained composite minimization problem whose objective function is possibly nonsmooth and nonconvex. Unlike the traditional construction of augmented Lagrangian function, we provide a proximal-perturbed augmented Lagrangian and then develop a new Bregman Alternating Direction Method of Multipliers (ADMM). Under mild assumptions, we show that the novel augmented … Read more

    An inexact ADMM for separable nonconvex and nonsmooth optimization

  • Jianchao Bai
  • Miao Zhang
  • Hongchao Zhang
    • Categories Nonsmooth Optimization, Quadratic Programming

    An Inexact Alternating Direction Method of Multiplies (I-ADMM) with an expansion linesearch step was developed for solving a family of separable minimization problems subject to linear constraints, where the objective function is the sum of a smooth but possibly nonconvex function and a possibly nonsmooth nonconvex function. Global convergence and linear convergence rate of the … Read more

    Double-proximal augmented Lagrangian methods with improved convergence condition

  • Jianchao Bai
    • Categories Complementarity and Variational Inequalities, Convex and Nonsmooth Optimization, Global Optimization Tags , , , ,

    In this paper, we propose a novel double-proximal augmented Lagrangian method(DP-ALM) for solving a family of linearly constrained convex minimization problems whose objective function is not necessarily smooth. This DP-ALM not only enjoys a flexible dual stepsize, but also contains a proximal subproblem with relatively smaller proximal parameter. By a new prediction-correction reformulation for this … Read more

    Generalized asymmetric forward-backward-adjoint algorithms for convex-concave saddle-point problem

  • Jianchao Bai
    • Categories Convex and Nonsmooth Optimization, Nonlinear Optimization Tags , ,

    The convex-concave minimax problem, also known as the saddle-point problem, has been extensively studied from various aspects including the algorithm design, convergence condition and complexity. In this paper, we propose a generalized asymmetric forward-backward-adjoint algorithm (G-AFBA) to solve such a problem by utilizing both the proximal techniques and the extrapolation of primal-dual updates. Besides applying … Read more

    Convergence analysis on a data-driven inexact proximal-indefinite stochastic ADMM

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

    In this paper, we propose an Inexact Proximal-indefinite Stochastic ADMM (abbreviated as IPS-ADMM) to solve a class of separable convex optimization problems whose objective functions consist of two parts: one is an average of many smooth convex functions and the other is a convex but potentially nonsmooth function. The involved smooth subproblem is tackled by … Read more

    Convergence analysis of an inexact relaxed augmented Lagrangian method

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

    In this paper, we develop an Inexact Relaxed Augmented Lagrangian Method (IR-ALM) for solving a class of convex optimization problems. Flexible relative error criteria are designed for approximately solving the resulting subproblem, and a relaxation step is exploited to accelerate its convergence numerically. By a unified variational analysis, we establish the global convergence of this … Read more

    An inexact ADMM with proximal-indefinite term and larger stepsize

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

    In this paper, an inexact Alternating Direction Method of Multipliers (ADMM) has been proposed for solving the two-block separable convex optimization problem subject to linear equality constraints. The first resulting subproblem is solved inexactly under relative error criterion, while another subproblem called regularization problem is solved inexactly by introducing an indefinite proximal term. Meanwhile, the … Read more