Bingsheng He

On the acceleration of augmented Lagrangian method for linearly constrained optimization

  • Bingsheng He
  • Xiao-Ming Yuan
    • Categories Convex Optimization Tags , ,

    The classical augmented Lagrangian method (ALM) plays a fundamental role in algorithmic development of constrained optimization. In this paper, we mainly show that Nesterov’s influential acceleration techniques can be applied to accelerate ALM, thus yielding an accelerated ALM whose iteration-complexity is O(1/k^2) for linearly constrained convex programming. As a by-product, we also show easily that … Read more

    An accelerated inexact proximal point algorithm for convex minimization

  • Bingsheng He
  • Xiao-Ming Yuan
    • Categories Convex Optimization Tags , , ,

    The proximal point algorithm (PPA) is classical and popular in the community of Optimization. In practice, inexact PPAs which solves the involved proximal subproblems approximately subject to certain inexact criteria are truly implementable. In this paper, we first propose an inexact PPA with a new inexact criterion for solving convex minimization, and show that the … Read more

    A splitting method for separate convex programming with linking linear constraints

  • Bingsheng He
  • Tao Min
  • Xiao-Ming Yuan
    • Categories Convex Optimization Tags , , , , ,

    We consider the separate convex programming problem with linking linear constraints, where the objective function is in the form of the sum of m individual functions without crossed variables. The special case with m=2 has been well studied in the literature and some algorithms are very influential, e.g. the alternating direction method. The research for … Read more

    Proximal alternating direction-based contraction methods for separable linearly constrained convex optimization

  • Bingsheng He
  • Peng Zheng
  • Wang XiangFeng
    • Categories Complementarity and Variational Inequalities, Convex Optimization Tags , , ,

    Alternating direction method (ADM) has been well studied in the context of linearly constrained convex programming problems. Recently, because of its significant efficiency and easy implementation in novel applications, ADM is extended to the case where the number of separable parts is a finite number. The algorithmic framework of the extended method consists of two … Read more

    The unified framework of some proximal-based decomposition methods for monotone variational inequalities with separable structure

  • Bingsheng He
  • Xiao-Ming Yuan
    • Categories Complementarity and Variational Inequalities Tags , , , ,

    Some existing decomposition methods for solving a class of variational inequalities (VI) with separable structures are closely related to the classical proximal point algorithm, as their decomposed sub-VIs are regularized by proximal terms. Differing in whether the generated sub-VIs are suitable for parallel computation, these proximal-based methods can be categorized into the parallel decomposition methods … Read more

    Alternating directions based contraction method for generally separable linearly constrained convex programming problems

  • Bingsheng He
  • Xiao-Ming Yuan
  • Min Tao
  • Minghua Xu
    • Categories Convex Optimization Tags , , , ,

    The classical alternating direction method (ADM) has been well studied in the context of linearly constrained convex programming problems and variational inequalities where both the involved operators and constraints are separable into two parts. In particular, recentness has witnessed a number of novel applications arising in diversified areas (e.g. Image Processing and Statistics), for which … Read more

    Proximal-like contraction methods for monotone variational inequalities in a unified framework

  • Bingsheng He
  • Lizhi Liao
  • Xiang Wang
    • Categories Complementarity and Variational Inequalities, Constrained Nonlinear Optimization, Convex Optimization Tags , ,

    Approximate proximal point algorithms (abbreviated as APPAs) are classical approaches for convex optimization problems and monotone variational inequalities. To solve the subproblems of these algorithms, the projection method takes the iteration in form of $u^{k+1} = P_{\Omega}[u^k-\alpha_k d^k]$. Interestingly, many of them can be paired such that $%\exists \tilde{u}^k, \tilde{u}^k = P_{\Omega}[u^k – \beta_kF(v^k)] = … Read more