• TITLE: Accelerated line-search and trust-region methods
• AUTHORS: P.-A. Absil, K. A. Gallivan
• ABSTRACT:
  In numerical optimization, line-search and trust-region methods are two important 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 general context of optimization on manifolds, of which optimization in $\rr^n$ 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
• STATUS: SIAM Journal on Numerical Analysis, Vol. 47, No. 2, pp. 997-1018, 2009

• Publisher's version: http://dx.doi.org/10.1137/08072019X [local copy]
• Tech report: http://www.optimization-online.org/DB_HTML/2008/04/1944.html

BibTeX citation:

@ARTICLE{AbsGal2009,
  author = "P.-A. Absil and K. A. Gallivan",
  title = "Accelerated line-search and trust-region methods",
  journal = "SIAM J. Numer. Anal.",
  fjournal = "SIAM Journal on Numerical Analysis",
  volume = 47,
  number = 2,
  year = 2009,
  pages = "997--1018",
}