Xiao-Ming Yuan

Positive-Indefinite Proximal Augmented Lagrangian Method and its Application to Full Jacobian Splitting for Multi-block Separable Convex Minimization Problems

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

    The augmented Lagrangian method (ALM) is fundamental for solving convex programming problems with linear constraints. The proximal version of ALM, which regularizes ALM’s subproblem over the primal variable at each iteration by an additional positive-definite quadratic proximal term, has been well studied in the literature. In this paper, we show that it is not necessary … Read more

    Improving an ADMM-like Splitting Method via Positive-Indefinite Proximal Regularization for Three-Block Separable Convex Minimization

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

    The augmented Lagrangian method (ALM) is fundamental for solving convex minimization models with linear constraints. When the objective function is separable such that it can be represented as the sum of more than one function without coupled variables, various splitting versions of the ALM have been well studied in the literature such as the alternating … Read more

    Linearized Alternating Direction Method of Multipliers via Positive-Indefinite Proximal Regularization for Convex Programming

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

    The alternating direction method of multipliers (ADMM) is being widely used for various convex minimization models with separable structures arising in a variety of areas. In the literature, the proximalversion of ADMM which allows ADMM’s subproblems to be proximally regularized has been well studied. Particularly the linearized version of ADMM can be yielded when the … Read more

    Faster Alternating Direction Method of Multipliers with a Worst-case O(1/n^2) Convergence Rate

  • Wenyi Tian
  • Xiao-Ming Yuan
    • Categories Convex Optimization Tags , , , ,

    The alternating direction method of multipliers (ADMM) is being widely used for various convex programming models with separable structures arising in specifically many scientific computing areas. The ADMM’s worst-case O(1/n) convergence rate measured by the iteration complexity has been established in the literature when its penalty parameter is a constant, where n is the iteration … Read more

    Convergence Analysis of ISTA and FISTA for “Strongly + Semi” Convex Programming

  • Ke Guo
  • Xiao-Ming Yuan
  • Shangzhi Zeng
    • Categories Convex Optimization Tags , , , , ,

    The iterative shrinkage/thresholding algorithm (ISTA) and its faster version FISTA have been widely used in the literature. In this paper, we consider general versions of the ISTA and FISTA in the more general “strongly + semi” convex setting, i.e., minimizing the sum of a strongly convex function and a semiconvex function; and conduct convergence analysis … Read more

    An Algorithmic Framework of Generalized Primal-Dual Hybrid Gradient Methods for Saddle Point Problems

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

    The primal-dual hybrid gradient method (PDHG) originates from the Arrow-Hurwicz method, and it has been widely used to solve saddle point problems, particularly in image processing areas. With the introduction of a combination parameter, Chambolle and Pock proposed a generalized PDHG scheme with both theoretical and numerical advantages. It has been analyzed that except for … Read more

    Infinite horizon optimal policy for an inventory system with two types of products sharing common hardware platforms

  • Mabel C. Chou
  • Chee-Khian Sim
  • Xiao-Ming Yuan
    • Categories Applications - OR and Management Sciences

    We consider a periodic review inventory system and present its optimal policy in the infinite horizon setting. The optimal inventory policy that maximizes the infinite horizon expected discount profit for the model is analytically obtained by relating to the finite horizon setting using results from variational analysis. Results are provided that elucidate the operations of … Read more

    Alternating Direction Method of Multipliers for Linear Programming

  • Bingsheng He
  • Xiao-Ming Yuan
    • Categories Linear Programming Tags , ,

    Recently the alternating direction method of multipliers (ADMM) has been widely used for various applications arising in scientific computing areas. Most of these application models are, or can be easily reformulated as, linearly constrained convex minimization models with separable nonlinear objective functions. In this note we show that ADMM can also be easily used for … Read more

    On the Step Size of Symmetric Alternating Directions Method of Multipliers

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

    The alternating direction method of multipliers (ADMM) is an application of the Douglas-Rachford splitting method; and the symmetric version of ADMM which updates the Lagrange multiplier twice at each iteration is an application of the Peaceman-Rachford splitting method. Sometimes the symmetric ADMM works empirically; but theoretically its convergence is not guaranteed. It was recently found … Read more

    On the Iteration Complexity of Some Projection Methods for Monotone Linear Variational Inequalities

  • Caihua Chen
  • Xiaoling Fu
  • Bingsheng He
  • Xiao-Ming Yuan
    • Categories Complementarity and Variational Inequalities Tags , , ,

    Projection type methods are among the most important methods for solving monotone linear variational inequalities. In this note, we analyze the iteration complexity for two projection methods and accordingly establish their worst-case O(1/t) convergence rates measured by the iteration complexity in both the ergodic and nonergodic senses, where t is the iteration counter. Our analysis … Read more