5 papers
A subspace method for large-scale trace ratio problems
G. Ferrandi, M. E. Hochstenbach, M. R. Oliveira
A subspace method is introduced to solve large-scale trace ratio problems. This approach is matrix-free, requiring only the action of the two matrices involved in the trace ratio.…
Limited memory gradient methods for unconstrained optimization
Giulia Ferrandi, Michiel E. Hochstenbach
The limited memory steepest descent method (Fletcher, 2012) for unconstrained optimization problems stores a few past gradients to compute multiple stepsizes at once. We review thi…
On the trace ratio method and Fisher's discriminant analysis for robust multigroup classification
Giulia Ferrandi, Igor V. Kravchenko, Michiel E. Hochstenbach +1
We compare two different linear dimensionality reduction strategies for the multigroup classification problem: the trace ratio method and Fisher's discriminant analysis. Recently,…
A homogeneous Rayleigh quotient with applications in gradient methods
Giulia Ferrandi, Michiel E. Hochstenbach
Given an approximate eigenvector, its (standard) Rayleigh quotient and harmonic Rayleigh quotient are two well-known approximations of the corresponding eigenvalue. We propose a ne…
A harmonic framework for stepsize selection in gradient methods
Giulia Ferrandi, Michiel E. Hochstenbach, Natasa Krejic
We study the use of inverse harmonic Rayleigh quotients with target for the stepsize selection in gradient methods for nonlinear unconstrained optimization problems. This provides…