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03 Apr 2008 Tech. Report UCL-INMA-2008-011 Accelerated line-search and trust-region methods
 

Summary: 03 Apr 2008 Tech. Report UCL-INMA-2008-011
Accelerated line-search and trust-region methods
P.-A. Absil
K. A. Gallivan
April 3, 2008
Abstract
In numerical optimization, line-search and trust-region methods are two im-
portant classes of descent schemes, with well-understood global convergence
properties. Here we consider "accelerated" versions of these methods, where
the conventional iterate is allowed to be replaced by any point that produces
at least as much decrease in the cost function as a fixed fraction of the decrease
produced by the conventional iterate. A detailed convergence analysis reveals
that global convergence properties of line-search and trust-region methods still
hold when the methods are accelerated. The analysis is performed in the gen-
eral context of optimization on manifolds, of which optimization in Rn
is a
particular case. This general convergence analysis sheds a new light on the
behavior of several existing algorithms.
Key words. line search, trust region, subspace acceleration, sequential subspace method, Riemannian
manifold, optimization on manifolds, Riemannian optimization, Arnoldi, Jacobi-Davidson, LOBPCG

  

Source: Absil, Pierre-Antoine - Département d'ingénierie Mathématique, Université Catholique de Louvain

 

Collections: Mathematics