Jianchao Bai

A projection algorithm based on KKT conditions for convex quadratic semidefinite programming with nonnegative constraints

  • Jianchao Bai
  • Chang Xiaokai
  • Liu Sanyang
    • Categories Linear, Cone and Semidefinite Programming Tags , , , ,

    The dual form of convex quadratic semidefinite programming (CQSDP) problem, with nonnegative constraints, is a 4-block separable convex optimization problem. It is known that,the directly extended 4-block alternating direction method of multipliers (ADMM4d) is very efficient to solve the dual, but its convergence is not guaranteed. In this paper, we reformulate the dual as a … Read more

    A One-Parameter Family of Middle Proximal ADMM for Constrained Separable Convex Optimization

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

    This work is devoted to studying a family of Middle Proximal Alternating Direction Method of Multipliers (MP-ADM) for solving multi-block constrained separable convex optimization. Such one-parameter family of MP-ADM combines both Jacobian and Gauss-Seidel types of alternating direction method, and proximal point techniques are only applied to the middle subproblems to promote the convergence. We … Read more

    Several variants of the primal-dual hybrid gradient algorithm with applications

  • Jianchao Bai
  • Jicheng Li
  • Zhie Wu
    • Categories Complementarity and Variational Inequalities, Convex Optimization

    By reviewing the primal-dual hybrid algorithm (PDHA) proposed by He, You and Yuan (SIAM J. Imaging Sci. 2014;7(4):2526-2537), in this paper we introduce four improved schemes for solving a class of generalized saddle-point problems. By making use of the variational inequality, weaker conditions are presented to ensure the global convergence of the proposed algorithms, where … Read more

    General parameterized proximal point algorithm with applications in the statistical learning

  • Jianchao Bai
  • Pingfan Dai
  • Jicheng Li
  • Jiaofen Li
    • Categories Convex and Nonsmooth Optimization, Statistics

    In the literature, there are a few researches for the proximal point algorithm (PPA) with some parameters in the proximal matrix, especially for the multi-objective optimization problems. Introducing some parameters to the PPA will make it more attractive and flexible. By using the unified framework of the classical PPA and constructing a parameterized proximal matrix, … Read more

    A Parameterized Proximal Point Algorithm for Separable Convex Optimization

  • Jianchao Bai
  • Jicheng Li
  • Hongchao Zhang
    • Categories Convex Optimization, Statistics

    In this paper, we develop a Parameterized Proximal Point Algorithm (P-PPA) for solving a class of separable convex programming problems subject to linear and convex constraints. The proposed algorithm is provable to be globally convergent with a worst-case $O(1/t)$ convergence rate, where $t$ is the iteration number. By properly choosing the algorithm parameters, numerical experiments … Read more

    Generalized Symmetric ADMM for Separable Convex Optimization

  • Jianchao Bai
  • Jicheng Li
  • Fengmin Xu
  • Hongchao Zhang
    • Categories Convex Optimization, Global Optimization Theory Tags , , , , , ,

    The Alternating Direction Method of Multipliers (ADMM) has been proved to be effective for solving separable convex optimization subject to linear constraints. In this paper, we propose a Generalized Symmetric ADMM (GS-ADMM), which updates the Lagrange multiplier twice with suitable stepsizes, to solve the multi-block separable convex programming. This GS-ADMM partitions the data into two … Read more