3 Presentations

• 
  09:00 AM - 09:25 AM

  The conjugate residual method in linesearch and trust-region methods

  • Marie-Ange Dahito, presenter, École polytechnique, Palaiseau

  Like the conjugate gradient method (CG), the conjugate residual method (CR) has desirable properties in linesearch and trust-region contexts for optimization. We investigate modifications that make CR suitable, even in the presence of negative curvature. CR performs as well as or better than CG, and yields savings in operator-vector products.
  Keywords: Conjugate Residual Method, Conjugate Gradient Method, Unconstrained Optimization
• 
  09:25 AM - 09:50 AM

  Globalization of high order methods

  • Samuel Goyette, presenter, Université de Sherbrooke
  • Jean-Pierre Dussault, Université de Sherbrooke
  • Dominique Orban, GERAD - Polytechnique Montréal

  We examine high-order optimization methods such as Chebyshev, Halley and Shamaanski's methods, which are extensions of Newton's method. We present a globalization of those methods based on a traditional trust-region scheme, and report convergence and numerical results.
  Keywords: Higher-Order Methods, Trust-Region Algorithms, Nonlinear Optimization
• 
  09:50 AM - 10:15 AM

  Scaled methods for computed tomography in cylindrical coordinates

  • Guillaume Mestdagh, presenter, Polytechnique Montréal

  Statistical X-ray computed tomography can lead to badly-scaled optimization problems with box constraints.
  We introduce modified versions of L-BFGS-B and TRON that use scaled directions to improve convergence without losing the simplicity of bound constraints. Results on simulated CT data are promising.
  Keywords: Imaging problems, Scaling, Projected Methods