l0-norm minimization

Complementarity Formulations of l0-norm Optimization Problems

  • Mingbin Feng
  • John E. Mitchell
  • Jong-Shi Pang
  • Xin Shen
    • Categories Complementarity and Variational Inequalities, Constrained Nonlinear Optimization Tags , ,

    In a number of application areas, it is desirable to obtain sparse solutions. Minimizing the number of nonzeroes of the solution (its l0-norm) is a difficult nonconvex optimization problem, and is often approximated by the convex problem of minimizing the l1-norm. In contrast, we consider exact formulations as mathematical programs with complementarity constraints and their … Read more

    Penalty Decomposition Methods for hBcNorm Minimization

  • Zhaosong Lu
  • Yong Zhang
    • Categories Applications - Science and Engineering, Nonlinear Optimization, Nonsmooth Optimization Tags , , , ,

    In this paper we consider general l0-norm minimization problems, that is, the problems with l0-norm appearing in either objective function or constraint. In particular, we first reformulate the l0-norm constrained problem as an equivalent rank minimization problem and then apply the penalty decomposition (PD) method proposed in [33] to solve the latter problem. By utilizing … Read more