4 Presentations

• 
  10:45 AM - 11:10 AM

  Some theory and algorithms for recovery of sparse integer-valued signals

  • Xiao-Wen Chang, presenter, McGill University

  In some applications the signal vector in a linear model is sparse and its entries are drawn from a finite alphabet following some distribution. We present some estimation theory and algorithms to recover the signal vector. Numerical examples are given to illustrate the effectiveness of the proposed algorithms.

  Key words: Parameter estimation, Integer least squares, l_0 norm regularization
• 
  11:10 AM - 11:35 AM

  The merits of keeping it smooth: Implementing a smooth exact penalty function for nonlinear programming

  • Ron Estrin, presenter, Stanford University

  We develop a factorization-free algorithm for constrained optimization based on a penalty function proposed by Fletcher (1970). This penalty was historically considered computationally prohibitive. However, we develop and efficient approach to evaluate the penalty by solving structured linear systems. We demonstrate the merits of this approach on some PDE-constrained optimization problems.

  Keywords: nonlinear programming, factorization-free, penalty method
• 
  11:35 AM - 12:00 PM

  Algorithm NCL for constrained optimization

  • Michael Saunders, presenter, Stanford University

  We reimplement the LANCELOT augmented Lagrangian method as a short
  sequence of nonlinearly constrained subproblems that can be solved
  efficiently by IPOPT and KNITRO, with warm starts on each subproblem.
  NCL succeeds on degenerate tax policy models that can't be solved directly.
• 
  12:00 PM - 12:25 PM

  Minimizing convex quadratics with variable precision Krylov methods

  • Ehouarn Simon, presenter, Université de Toulouse, INP, IRIT
  • Serge Gratton, Université de Toulouse, INP, IRIT
  • Philippe L. Toint, University of Namur

  Iterative algorithms for the solution of convex quadratic optimization problems are investigated, which exploit inaccurate matrix-vector products. Theoretical bounds on the performance of a Conjugate Gradients and a Full-Orthogonalization methods and new practical algorithms are derived. Numerical experiments suggest that these methods have significant potential, notably in the context of multi-precision computations.

  Keywords: convex quadratic optimization, variable accuracy, multi-precision arithmetic