Jean-Pierre Dussault

A new family of high order directions for unconstrained optimization inspired by Chebyshev and Shamanskii methods

  • Jean-Pierre Dussault
  • Bilel Kchouk
    • Categories Nonlinear Optimization, Unconstrained Optimization

    The 1669-1670 Newton-Raphson’s method is still used to solve equations systems and unconstrained optimization problems. Since this method, some other algorithms inspired by Newton’s have been proposed: in 1839 Chebyshev developped a high order cubical convergence algorithm, and in 1967 Shamanskii proposed an acceleration of Newton’s method. By considering a Newton-type methods as displacement directions, … Read more

    Local path-following property of inexact interior methods in nonlinear programming

  • Paul Armand
  • Jean-Pierre Dussault
  • Joël Benoist
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags , , , , ,

    We study the local behavior of a primal-dual inexact interior point methods for solving nonlinear systems arising from the solution of nonlinear optimization problems or more generally from nonlinear complementarity problems. The algorithm is based on the Newton method applied to a sequence of perturbed systems that follows by perturbation of the complementarity equations of … Read more

    Metal Artefact Reduction by Least-Squares Penalized-Likelihood Reconstruction with a Fast Polychromatic Projection Model

  • Jean-Pierre Dussault
  • Yves Goussard
  • Benoit Hamelin
    • Categories Biomedical Applications, Bound-constrained Optimization Tags , , , , ,

    We consider penalized-likelihood reconstruction for X-ray computed tomography of objects that contain small metal structures. To reduce the beam hardening artefacts induced by these structures, we derive the reconstruction algorithm from a projection model that takes into account the photon emission spectrum and nonlinear variation of attenuation to photon energy. This algorithm requires excessively long … Read more

    On the Stopping Criterion for Numerical Methods Used to Solve Linear Systems with Additive Gaussian Noise

  • Jean-Pierre Dussault
  • Yves Goussard
  • Benoit Hamelin
    • Categories Statistics, Unconstrained Optimization Tags , , , ,

    We consider the inversion of a linear operator with centered Gaussian white noise by MAP estimation with a Gaussian prior distribution on the solution. The actual estimator is computed approximately by a numerical method. We propose a relation between the stationarity measure of this approximate solution to the mean square error of the exact solution. … Read more