Approximate invariant subspaces and quasi-newton optimization methods

Authors:
Serge Gratton;Philippe L. Toint
Affiliations:
Centre National d'Etudes Spatiales (CNES), Toulouse, France,CERFACS, Toulouse, Cedex 01, France;Department of Mathematics, University of Namur - FUNDP, Namur, Belgium
Venue:
Optimization Methods & Software
Year:
2010

Citing 0
Cited 2

A Line Search Multigrid Method for Large-Scale Nonlinear Optimization

SIAM Journal on Optimization
Using approximate secant equations in limited memory methods for multilevel unconstrained optimization

Computational Optimization and Applications

Quantified Score

Hi-index	0.00

Visualization

Abstract

New approximate secant equations are shown to result from the knowledge of (problem dependent) invariant subspace information, which in turn suggests improvements in quasi-Newton methods for unconstrained minimization. A new limited-memory Broyden-Fletcher-Goldfarb-Shanno using approximate secant equations is then derived and its encouraging behaviour illustrated on a small collection of multilevel optimization examples. The smoothing properties of this algorithm are considered next, and automatic generation of approximate eigenvalue information demonstrated. The use of this information for improving algorithmic performance is finally investigated on the same multilevel examples.