Peng Dingtao

Singular value half thresholding algorithm for lp regularized matrix optimization problems

  • Peng Dingtao
    • Categories Nonsmooth Optimization, Unconstrained Optimization Tags , , , ,

    In this paper, we study the low-rank matrix optimization problem, where the penalty term is the $\ell_p~(0<p<1)$ regularization. Inspired by the good performance of half thresholding function in sparse/low-rank recovery problems, we propose a singular value half thresholding (SVHT) algorithm to solve the $\ell_p$ regularized matrix optimization problem. The main iteration in SVHT algorithm makes … Read more

    Fixed point continuation algorithm with extrapolation for Schatten p-quasi-norm regularized matrix optimization problems

  • Peng Dingtao
    • Categories Nonsmooth Optimization, Unconstrained Optimization Tags , , , ,

    In this paper, we consider a general low-rank matrix optimization problem which is modeled by a general Schatten p-quasi-norm (${\rm 0<p<1}$) regularized matrix optimization. For this nonconvex nonsmooth and non-Lipschitz matrix optimization problem, based on the matrix p-thresholding operator, we first propose a fixed point continuation algorithm with extrapolation (FPCAe) for solving it. Secondly, we … Read more

    Continuous exact relaxation and alternating proximal gradient algorithm for partial sparse and partial group sparse optimization problems

  • Peng Dingtao
    • Categories Nonsmooth Optimization, Unconstrained Optimization Tags

    In this paper, we consider a partial sparse and partial group sparse optimization problem, where the loss function is a continuously differentiable function (possibly nonconvex), and the penalty term consists of two parts associated with sparsity and group sparsity. The first part is the $\ell_0$ norm of ${\bf x}$, the second part is the $\ell_{2,0}$ … Read more

    S_1/2 Regularization Methods and Fixed Point Algorithms for Affine Rank Minimization Problems

  • Peng Dingtao
  • Yu Jian
  • Naihua Xiu
    • Categories Linear, Cone and Semidefinite Programming, Nonsmooth Optimization

    The affine rank minimization problem is to minimize the rank of a matrix under linear constraints. It has many applications in various areas such as statistics, control, system identification and machine learning. Unlike the literatures which use the nuclear norm or the general Schatten $q~(0<q<1)$ quasi-norm to approximate the rank of a matrix, in this … Read more