ill-conditioned problems

Performance of First- and Second-Order Methods for L1-Regularized Least Squares Problems

  • Kimon Fountoulakis
  • Jacek Gondzio
    • Categories Convex and Nonsmooth Optimization Tags , , , ,

    We study the performance of first- and second-order optimization methods for l1-regularized sparse least-squares problems as the conditioning and the dimensions of the problem increase up to one trillion. A rigorously defined generator is presented which allows control of the dimensions, the conditioning and the sparsity of the problem. The generator has very low memory … Read more

    Regularization Using a Parameterized Trust Region Subproblem

  • Oleg Grodzevich
  • Henry Wolkowicz
    • Categories Applications - Science and Engineering, Biomedical Applications, Nonlinear Systems and Least-Squares Tags , , , ,

    We present a new method for regularization of ill-conditioned problems, such as those that arise in image restoration or mathematical processing of medical data. The method extends the traditional {\em trust-region subproblem}, \TRS, approach that makes use of the {\em L-curve} maximum curvature criterion, a strategy recently proposed to find a good regularization parameter. We … Read more