Peng Jian-Wen

Linear Convergence Rate of the Generalized Alternating Direction Method of Multipliers for a Class of Convex Optimization Problems

  • Peng Jian-Wen
  • Xue-Qing Zhang
    • Categories Convex and Nonsmooth Optimization Tags , , ,

    Rencently, the generalized aternating direction method of multipliers (GADMM) proposed by Eckstein and Bertsekas has received intensive attention from a broad spectrum of areas. In this paper, we consider the convergence rate of GADMM when applying to the convex optimization problems that the subdifferentials of the underlying functions are piecewise linear multifunctions, including LASSO, a … Read more

    Linearized version of the generalized alternating direction method of multipliers for three-block separable convex minimization problem

  • Peng Jian-Wen
  • Xue-Qing Zhang
    • Categories Convex Optimization

    Recently, the generalized alternating direction method of multipliers (GADMM) proposed by Eckstein and Bertsekas has received wide attention, especially with respect to numerous applications. In this paper, we develop a new linearized version of generalized alternating direction method of multipliers (L-GADMM) for the linearly constrained separable convex programming whose objective functions are the sum of … Read more

    Iteration complexity on the Generalized Peaceman-Rachford splitting method for separable convex programming

  • Peng Jian-Wen
  • Xue-Qing Zhang
    • Categories Convex Optimization

    Recently, a generalized version of Peaceman-Rachford splitting method (GPRSM) for solving a convex minmization model with a general separable structure has been proposed by \textbf{Sun} et al and its global convergence has been proved. In this paper, we further study theoretical aspects of the generalized Peaceman-Rachford splitting method. We first establish the worst-case $\mathcal{O}(1/t)$ convergence … Read more

    Optimality conditions of set-valued optimization problem involving relative algebraic interior in ordered linear spaces

  • Peng Jian-Wen
  • Xinmin Yang
  • Zhou Zhi-Ang
    • Categories Generalized Convexity/Monoticity, Multi-Criteria Optimization Tags

    In this paper, firstly, a generalized subconvexlike set-valued map involving the relative algebraic interior is introduced in ordered linear spaces. Secondly, some properties of a generalized subconvexlike set-valued map are investigated. Finally, the optimality conditions of set-valued optimization problem are established. Citation {\bf AMS 2010 Subject Classifications:} 90C26, 90C29, 90C30ArticleDownload View PDF