Shujun Shujun

A globally and linearly convergent PGM for zero-norm regularized quadratic optimization with sphere constraint

  • Shaohua Pan
  • Shujun Shujun
  • Wu Yuqia
    • Categories Bound-constrained Optimization

    This paper is concerned with the zero-norm regularized quadratic optimization with a sphere constraint, which has an important application in sparse eigenvalue problems. For this class of nonconvex and nonsmooth optimization problems, we establish the KL property of exponent 1/2 for its extended-valued objective function and develop a globally and linearly convergent proximal gradient method … Read more

    GEP-MSCRA for computing the group zero-norm regularized least squares estimator

  • Shaohua Pan
  • Shujun Shujun
    • Categories Nonsmooth Optimization, Statistics

    This paper concerns with the group zero-norm regularized least squares estimator which, in terms of the variational characterization of the zero-norm, can be obtained from a mathematical program with equilibrium constraints (MPEC). By developing the global exact penalty for the MPEC, this estimator is shown to arise from an exact penalization problem that not only … Read more

    Error bounds for rank constrained optimization problems and applications

  • Shaohua Pan
  • Shujun Shujun
    • Categories Applications - OR and Management Sciences Tags , , ,

    This paper is concerned with the rank constrained optimization problem whose feasible set is the intersection of the rank constraint set $\mathcal{R}=\!\big\{X\in\mathbb{X}\ |\ {\rm rank}(X)\le \kappa\big\}$ and a closed convex set $\Omega$. We establish the local (global) Lipschitzian type error bounds for estimating the distance from any $X\in \Omega$ ($X\in\mathbb{X}$) to the feasible set and … Read more

    Exact penalty decomposition method for zero-norm minimization based on MPEC formulation

  • Xiaolan Liu
  • Shaohua Pan
  • Shujun Shujun
    • Categories Applications - OR and Management Sciences Tags , , ,

    We reformulate the zero-norm minimization problem as an equivalent mathematical program with equilibrium constraints and establish that its penalty problem, induced by adding the complementarity constraint to the objective, is exact. Then, by the special structure of the exact penalty problem, we propose a decomposition method that can seek a global optimal solution of the … Read more