Lifeng Chen

Fixed point and Bregman iterative methods for matrix rank minimization

  • Shiqian Ma
  • Donald Goldfarb
  • Lifeng Chen
    • Categories Convex and Nonsmooth Optimization, Convex Optimization, Nonsmooth Optimization Tags , , , , ,

    The linearly constrained matrix rank minimization problem is widely applicable in many fields such as control, signal processing and system identification. The linearly constrained nuclear norm minimization is a convex relaxation of this problem. Although it can be cast as a semidefinite programming problem, the nuclear norm minimization problem is expensive to solve when the … Read more

    Interior-Point l_2 Penalty Methods for Nonlinear Programming with Strong Global Convergence Properties

  • Lifeng Chen
  • Donald Goldfarb
    • Categories Nonlinear Optimization Tags , , , , ,

    We propose two line search primal-dual interior-point methods that approximately solve a equence of equality constrained barrier subproblems. To solve each subproblem, our methods apply a modified Newton method and use an $\ell_2$-exact penalty function to attain feasibility. Our methods have strong global convergence properties under standard assumptions. Specifically, if the penalty parameter remains bounded, … Read more